It’s interesting. Chin-ups, that is with the palms facing the body, tend to be easier than pullups, with the palms facing away. But for some reason, when doing a high rep set I tend to max out around the same number.
Just this past weekend I pulled off 22 chin-ups, which is an all-time record (my previous best being 21 reps).
Oh, and these are quite strict going for throat to bar (which is a measure that works a bit better than chin over bar). They are full range when many people cut that range short.
And if you want the roadmap from how I went to not being able to budge an inch on a pullup bar to doing this, check out The Ultimate Guide to Pullups and Chin-ups.