If portability is high priority for you, you should definitely consider mirrorless. This said, there are some trade-offs with current mirrorless technology that may make a small SLR body a better fit for your needs; it depends a lot on what you want to shoot. I shoot a lot of wildlife and action, so a true TTL OVF is important for me. This pretty much eliminates mirrorless as an option for my primary body. Mirrorless bodies also generally lag SLRs in autofocus speed, which is another important feature for wildlife and action shooting. It doesn't matter how good the IQ is otherwise if the AF didn't rack fast enough to keep that flying bird in focus
This said, if I could afford it, I'd love to have a decent mirrorless as a complementary body to my DSLR, but my budget doesn't allow this at present.
Assuming your choice remains between the SL1 and the D3300, the best thing do is go to a good store that will let you handle and shoot with the demo models (or, even better, find one of each that you can borrow or rent for a day). Stats like megapixels, fps, and dynamic range are all well and good, but there are also some important differences to the way Canon and Nikon do the physical layout and UI; you may find that you have a distinct preference for one system or the other.
Beyond this, I will speak only to the Canon since I'm a Canon shooter and don't have much experience with Nikons. The SL1 is basically a T2i shrunk down into a smaller body. This isn't necessarily a bad thing; the T2i was (and still is) as solid beginner SLR. If I could afford it, I'd love to have an SL1 body to use as a smaller, lighter secondary body, especially since the SL1 can use my current Canon EF lenses without having to fiddle with an adapter or anything like that.
I think whether the SL1 a good choice as a beginner SLR depends a lot on where you imagine yourself going in the future. If you like the Canon system and see yourself investing in multiple lenses, and down the road a larger, higher performance body either as an upgrade or in addition to the SL1, then I think the SL1 is a good place to start as you'll be able to trade up bodies without changing your entire lens collection as well, or having to deal with adapters. But I'm not sure it's a particularly strong choice if you anticipate just buying the SL1 and sticking with it as your one-and-only camera body for many years to come.