With a DSLR or a Sony SLT, the lens you use will make a MUCH bigger difference in terms of low light performance, especially with the lower-priced bodies. Pretty much any DSLR/Sony SLT will do a decent job in low light provided that you've got suitable glass in front of it.
If you go down that route, what you will probably need is a lens with a large aperture (most recommend f/2.8 though f/4.0 may work depending on how much light there is) as a larger aperture allows you to run a lower ISO number, reducing the likelihood of noisy images. You can also shoot at higher shutter speeds, reducing the likelihood of blurring too. The downside is that as you'd expect, that large aperture will usually cost you.
DSLRs: Canon EOS 7D Mark II, Canon EOS 70D
CSC: Canon EOS M3
Lenses: Canon EF-S 15-85mm f/3.5-5.6 IS USM, EF 50mm f/1.8 II, EF 100-400mm f/4.5-5.6L IS USM, Canon EF-M 18-55mm f/3.5-5.6 IS STM, Canon EF-M 22mm f/2.0 STM