First of all, I would say that part of the problem exists in how you described them: "cute but onery" 3 year old and "adorable" (like he could do no wrong) 11 month old. That your younger one "likes to take toys away" but that the older one is "in a very horrible temper tantrum stage". Now, that's just what you said here, but I will (nicely) remind you that if it's said to ANYONE in public, that your older one probably knows this and POSSIBLY feels inferior already. Chastising him only helps further this notion, and the shoving and hitting is probably a way to punish the younger one because he doesn't think you'll handle it.
I know that 11 months old is way too young to know better and WAY too young to be doing it purposely, but as the oldest child (of 4, 2 girls and 2 boys!) I also know that if you do not try to handle this problem from BOTH sides early on, then the older one will just continue to be resentful, and the younger one will grow to use that opportunity to walk all over you and the older one. Punishing after the fact for something they've always gotten away with doesn't really help, either, when they're teens.
Now, for the most part, I get on well with my siblings (we're adults now, so that helps! *grin*), but growing up was ...well, it was hell in these situations...mostly because my parents took the stance that since I was older, I should know better, and help them teach the younger one. That might work when they're young, but by the time they're nearing elementary school age, it begins to rub of favoritism. PLUS, if the younger child acts up, the older child will sometimes transfer those failure feelings on themselves as well, as they'd possibly TRIED to show good behavior.
My solution would be to have your 3 year old pick out a couple of his toys that are "his only", and then allow your 11 month old to play with all but those toys (gently take them away and put them up, as you would anything else he shouldn't get into), and then talk to your 3 year old about how babies get into things, and how if he needs private time to play with something, that you should be told so that you can engage the younger one in something else. But be sure to spend some private time (when you can - naptime or bedtime or whatnot) with the older one so he doesn't feel left out.
Establishing fairness early on will help combat those "troublesome" actions, but looking at it from the older one's point of view is the most important thing - too many parents I know were never in that position, and so they look at it from the younger one's point of view because the younger one is usually "unable to help him/herself". Also remember, finally, that boys play differently than girls - a LOT of pushing and all - and you'll have your hands full when they're older. Enjoy the serenity while you have it! *grin*