Best option is to always go to the store and play with them to see which suits you better. Or even go and play with others in your price range! Explore other cameras that aren't in your budget!
Realistically, there isn't much to say on one system over another at that price point. But at any price point, it'll come down to what matters to you, personally. Both are great systems, both have their pros and cons. I'd suggest doing a fair amount of research before committing. Speaking of just that, remember that you're buying into a system. Look at available lenses and other things like external flashs that you MAY want in the future.
I shot on Canon for years, but always hated their button and wheel layout. Back in I think it was 2005, I switched to Nikon. Infinitely more comfortable to me. But the thing is, EVERYTHING IS A TRADE-OFF. Again, it's all about what matters to you. I'll take size over portability any day of the week. Shooting comfortably has become very important to me, especially in this past year where I've experienced quite a few issues with my hands. Turns out I have localized Fibromyalgia. Yeah. Comfort over weight for me. But that's me. You may think differently.
I have extensive experience with both cameras you're looking at, and though I'm a Nikon guy, I'll never tell someone to buy Nikon gear just because. I actually really like Canon gear as well. My ex-business partner used two of the SL1's for her shooting. To be honest about the SL1, It's a VERY fun camera to shoot on...but it's tiny. If you have bigger hands, you'll hate it. I have, I suppose, normal sized hands. I wear size large gloves. I borrowed one for a day and after a day of shooting on it, my hands were cramped! My partner was a woman...5 feet all. Tiny hands. She was comfortable with it.
My wife uses the D3300. While it's still small, it's not uncomfortable after a long period of time.
Both cameras have great image quality. I won't complain about either.