The only downside of Easy mode is your inability to do the Easter egg. I guess you could also say it doesn't count twords Leaderboards (Actual maximum rounds on a map) also, but no custom games do anyway.
You can bank money, get your personal leaderboards up (Kills, Perks, Grenade kills, etc) up, get your K/D up, and even RANK UP. Yes you can rank all the way to shotguns playing nothing but easy. Honestly the only thing I notice in easy that is different is the speed in which they run, and the round they actually start running at you. Good for more relaxing gameplay rounds 10 and below for newer people, and easier in high rounds due to a speed cap when they run at you.