Question: "I often hear sin is sin and no sin is greater than another. What's the church's stance on this particular subject?"
We see that there are degrees of sin very clearly in Scripture. For example, in Numbers 15:22-31, we are told about a general sacrifice that was offered for the unintentional sins of the people, and individuals who became aware of an unintentional sin could make an individual offering, But then it says that those who have sinned "presumptuously" (which in Hebrew literally means "with a raised hand") are not covered by these sacrifices.
You also see that different kinds of sins are dealt with very differently in the canons. Some sins can warrant very lengthy excommunications, but then when it comes to other sins, one simply needs to confess the sin, and no penance would be necessary. It would be ridiculous, for example to not recognize that there is a significant difference between mass murder, and someone briefly having an unchristian thought about another person. Of course even the most minor sins need to be repented of, and we should never excuse ourselves and ignore them, but both Scripture and Tradition recognize that not all sins are equal in their seriousness.
St. Nikodemus of the Holy Mountain explains in chapter 3 of the Exomologetarion (A Manual of Confession):
Concerning these you must know that, just as a physician is required to know what the illnesses of the body are in order to treat them, you who seek to be a Spiritual Father are obligated to know what the illnesses of the soul are, that is, sins, in order to treat them. Although the illnesses of the soul are many, they generally fall into the following three categories. Hence, you need to know which are mortal, which are pardonable and not mortal, and which are sins of omission or inaction.
1. Concerning Mortal Sins
According to Gennadios Scholarios, George Koressios, the Orthodox Confession, and Chrysanthos of Jerusalem, mortal sins are those voluntary sins which either corrupt the love for God alone, or the love for neighbor and for God, and which render again the one committing them an enemy of God and liable to the eternal death of hell.  Generally speaking, they are: pride, love of money, sexual immorality, envy, gluttony, anger, and despondency, or indifference. 
2. Concerning Pardonable Sins
Pardonable sins are those voluntary sins which do not corrupt the love for God or the love for neighbor, nor do they render the person an enemy of God and liable to eternal death, to which transgressions even the Saints are susceptible, according to the words of the Brother of God: “For in many things we all sin” (Jas. 3:2), and of John: “If we say that we have no sin, we deceive ourselves” (l Jn. 1:8), and according to Canons 125, 126, and 127 of Carthage. These sins, according to Koressios and Chrysanthos, are: idle talk, the initial inclination and agitation of anger, the initial inclination of lust, the initial inclination of hate, a white lie, passing envy, or that which is commonly called jealousy, which is slight grief over the good fortunes of one’s neighbor, and the like. 
Know also, Spiritual Father, that the many sins which are generally called pardonable are not of one and the same degree, but they are of varying degrees, smaller and larger, lower and higher, and that pardonable sins and mortal sins are two extremes. For in between these extremes there are found varying degrees of sins, beginning from the pardonable ones and proceeding up to the mortal ones, which degrees were not given names by the Ancients, perhaps because they are many and varied according to the class and specific kind of sins, but could have named them if they so desired. Here we name some of them, for the benefit of clarity and for your knowledge, beginning from below: pardonable sins, those near the pardonable, those that are non-mortal, those near the non-mortal, those between the non-mortal and the mortal, those near the mortal, and finally, mortal sins. Here is an example of the sins of the incensive aspect of the soul: The initial movement of anger is pardonable; near to the pardonable is for someone to say harsh words and get hot-tempered. A non-mortal sin is to swear; near the non-mortal is for someone to strike with the hand. Between the non-mortal and the mortal is to strike with a small stick; near the mortal is to strike with a large stick, or with a knife, but not in the area of the head. A mortal sin is to murder. A similar pattern applies to the other sins. Wherefore, those sins nearer to the pardonable end are penanced lighter, while those nearer to the mortal end are more severely penanced. 
3. Concerning Sins of Omission
Those good works, or words, or thoughts, which are capable of being done or thought by someone, but through negligence were not done, or said, or thought, are called sins of omission,  and are brought forth from the mortal sin of despondency, as we have said. I know very well that these sins of omission are not considered by people as full sins, because those are few who consider it a sin if they did not perform such and such a charity when they were able to, or had the means to either give good advice to their neighbor, or to do a certain amount of prayer, or do another virtue, and did not.
But this, however, I know for certain, that God will render an account on the day of judgment concerning these. Who verifies this for us? The example of that slothful servant who had the one talent and buried it in the ground, who was judged, not because he committed any sin or injustice with it (because he who gave the talent to him took it all back, as Basil the Great says in the Introduction of The Long Rules),  but because being able to increase it, was negligent and did not increase it: “Thou oughtest therefore to have put my money to the exchangers, and then at my coming I should have received mine own with usury” (Mt. 25:27). It is also verified for us by the example of the five foolish virgins who were condemned for nothing other than an absence of oil. And concerning the sinners placed at the left hand, they will be condemned, not because they committed any sin, but because they were lacking and were not merciful to their brother: “For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink” (Mt. 25:42). The reason that God gave to man natural strength was not in order to leave it idle and useless, without results and fruit, just as that slothful servant left the talent of the Lord idle, as we said above, but He gave it to man in order for man to put it into action, and into practice, and for it to increase, doing good with it and the commandments of the Lord, and so to be saved through this. On this account Basil the Great said: “We have already received from God the power to fulfill all the commandments given us by Him, so that we may not take our obligation in bad part, as though something quite strange and unexpected were being asked of us, and that we may not become filled with conceit, as if we were paying back something more than had been given us.”  And also in agreement with the above words, his brother, Gregory of Nyssa, says: “As each shall receive his wages, just as the Apostle says (1 Cor. 3:14), according to his labor, so also each shall receive punishment according to the extent of their negligence.” 
Those things which are also called sins of omission are those which we were able to prevent, by word or act, but did not prevent. On this account those who commit these are likewise penanced according to Canon 25 of Ancyra, Canon 71 of Basil the Great, and Canon 25 of St. John the Faster. 
Furthermore, Spiritual Father, you must know that the degrees of sin from the beginning until the end are twelve. The first degree is when someone does good, but not in a proper manner, mixing the good with the bad. This occurs in seven ways, as Basil the Great says, “As regards the place, the time, the person, the matter involved, or in a manner intemperate, or disorderly, or with improper dispositions.”  An example of a sin of the first degree is when someone performs an act of mercy, or fasts, or does some other good deed, so that he might be glorified by people. The second degree of sin is complete idleness in regard to the good. The third degree is an assault of evil. The fourth is coupling. The fifth is struggle.  The sixth is consent.  The seventh is the sin according to the intellect, according to St. Maximos, which is when a person, having consented, plans carefully to accomplish that sin which is in his intellect so as to do the deed. The eighth is the deed itself and the sinful act. The ninth is the habit of someone committing the sin often. The tenth is the addiction to sin, which with violence and force compels the person to sin voluntarily and involuntarily. The eleventh is despair, that is, hopelessness. The twelfth is suicide, namely, for a person to kill himself, while having a sound intellect, being conquered by despair. So then, Spiritual Father, you must try assiduously in every way to turn the sinner around to smaller degrees of sin and to prevent him from proceeding to the greater degrees ahead. And most of all, you must endeavor to sever him from despair, no matter in how great a degree of sin he is found.