My experience is primarily with canon. I own both a t3i and a 7d and for me the 7d is perfect for my youtube greenscreening. Although, I will say that I purchased both of these cameras before the release of the GH4 and now regret it.
After getting some face time with a GH3 and noticing the difference, I really think for its price range, it is the king. The only downside is not being able to use canon glass without an adapter. I prefer canon glass, but if you're only going to be using the kit lens anyways, then it won't be too big of a problem since the kits are similar across the board.
Long story short, I'd either get the GH3 with a kit lens, or a t3i and a decent canon lens. Both should keep you in your budget.