I think some of the disadvantages of large schools can be counteracted by them splitting them further.
I went to a small secondary and, for example, issues would go form teacher, deputy, head.
My dc's very large secondary is split into years and upper/lower school (10/11 & 7/8/9)
so issues go: form teacher, head of year, head of lower/upper school, deputy, head.
It's all very well to say there's more likelihood of finding like minded children in a large school, but they may never venture far enough to find them-or they may just pass like ships in the night, particularly if shy.
The cliques tend to be the same, just more of them.
Some large schools are great at SEN as they have a good department to support them. Others find they can basically ignore them until they get so bad they either drop out voluntarily or they have to do something.
There's usually more extra curriculum things at a large school-the large juniors mine were at have 3-4 clubs run by the school every day.
Things like teams can be better-but you've less chance of getting in. So if you're interested in playing for a winning team, and you're good, that's great, if you just want to have a go you may just never get a chance.