Took my A6000 and my T3i on a trip to Nice, France.
The kit lens (16-50) on the Sony seems inconsistent, but sometimes it does pretty well. Maybe it's just me. A larger max aperture lens would be my next acquisition for low light, although the Sony seems happier at higher ISO's than the T3i, which sort of makes up for some of it. I had a Canon f1.8 50 with me but it seemed too long a focal length for some things, and didn't autofocus well in anything but bright light on the Sony.
I used the Sony much more than the T3i mostly because it was so much smaller and lighter, I had a Sigma 10-20 on the Canon which made the combo surprisingly heavy.