Different program sizes have different "feels" to them, and it has practical effects like how the call system works, night float, jeopardy, how vacation time is scheduled, etc.
I interviewed at programs that ranged in size from 8 in the incoming class, at the smallest, to at least 40. Maybe larger, I can't recall.
It makes a big difference if people get pregnant or resign, for example, how the extra work is distributed.
At one program if there are any clashes in personality with uppers, you're sorta screwed. At the same time, other programs you could go through the whole residency and have some folks you've never worked with, or like every rotation you're working with someone new to you. That can feel isolating, but it also gives you a cleaner slate as you go through.
It's easier to get lost and not get as much guidance in a bigger program, and that can affect how well you're trained. At the same time, while smaller programs will try to sell you on all the "extra" personal attention you get, that can be a double edged sword.
Often how large the program is, will be related to what sort of clinical exposure you'll get. Really big programs tend to be associated with larger institutions and can be a lot busier, and can affect what patient demographic you get. Smaller programs tend to be more associated with community programs, and that's a bit different feel as well.
It makes a difference with the gossip mill. In a small program everyone knows everything. In a larger program some people might not even know your face if they do know your name.
It's definitely one of many factors that makes a difference to your training. People come out of all programs trained to do their job, though. It's just a question of what path that takes.