I will attempt to answer your question. I made the following assumptions based on your question:
1. A full squat means that you squat down as far as possible.
2. A parallel squat means that a line passing through your knee and hip joint would be parallel to the ground.
Now, based on my assumptions above, I will attempt to answer which is better: full or parallel? But first, let me toss this out to you and everyone reading this post: Why not include these positions as well?
1. 1/4 inch above full
2. 1/2 inch above full
3. 1-5/16 inches above full
4. 1/3 inch below parallel
5. 7/8 inch below parallel
6. 1-5/7 inches below parallel
7. 11/22 inch above parallel
8. 8/9 inch above parallel
9. 1-13/17 inches above parallel
.
.
.
As you can see, this list could go on ad nauseam. But why did I bother to create this list? The point is this: There is nothing under the sun that is magical about performing the squat at "exactly" the full or parallel positions. You know that and I know that. There are an infinite number of positions to choose in the squat training range. In other words, IMO, don't get hung up on whether you are going to full or parallel.
But Max, you say, what's the answer then? The answer is this: listen to your body. If it hurts to squat at a specific position or range, then don't train in that range. Just remember this, if you are making great progress at 1/2 inch above parallel, who cares if you are not exactly parallel? If you are making great progress at 2/3 inch above full, who cares if you are not going to the full position? Listen to your body.