You have a problem that many people here have. You love your primary camera but you eventually get tired of the size when trying to use it as a casual walkaround camera. Many of us, including myself, come to this point. You will get lots of advice here, but you will most likely need to test a few before you find that light walkaround camera you are looking for.
First thing to accept - IT WILL NOT BE AS GOOD AS YOUR PRIMARY CAMERA. There WILL be some differences and compromises
If they could make a 5d3 the size of a cell phone, they already would have.
Once you accept that, you can focus on the main reason you are looking for a different camera - compact & light
The reality of it, for me, is that 90% of my walkaround photos are actually taken with my phone. I actually wanted a camera the size of my phone that performed like a dslr. That obviously wasn't going to happen. so...
After testing a few mirrorless cameras, point and shoots, bridge cameras, I ended up with a canon SL1. I know it is not as small as a mirrorless, but it is a TINY DSLR and I can use my current lenses without an adapter. I pair it w the canon 24mm 2.8 pancake lens and it is a great walkaround combo. That combo also only cost me about $400. The performance of this combo vastly outweighs the cost.
You will most likely come to a different conclusion to your problem than I did, but this works for me.
for differences between crop & FF and mirrorless, search the forum, there are a TON of threads already.
As far as printing, you will be fine with whatever you get.