I read that there are some different traditions (croquet, carrying the football for army/navy) but are the companies collectively very different from one another? If so how? And how does it come about?
If there are things about your company you don't like, you'll have the opportunity to change them. Not during plebe summer or plebe year, but as time goes on. That's one of the reason the lists of company traits are pretty useless - as one group of firsties leaves and the next takes over, the character of a company can change dramatically. Same if the cadre changes.