Assuming you already have a good lens(or have a separate budget for that) - look for a camera with the biggest sensor. Full Frame, preferably. The greater the sensor size the better(less intensive) the shot noise becomes. To put it in simple words: more area - more light - less noise.
AFAIK the Sony A850 is the only Full Frame that would fit your budget but I might be wrong. Please do some research on that before buying, I only did a quick google search.
But if it's too much of a stretch just go for APS-C (or any equivalent) but definitely not lower. As others have said - a good lens is key. It is better to buy a cheaper camera and a good lens than the other way around.
Your old camera had an APS-C sized sensor, but it was also a camera introduced in 2013 so any newer camera should outperform it. With that said, though, it also depends what kind of lenses you've been using with it.
If I were to put it in numbers then it's like a 80-20, Lens-To-Body-Ratio. If we talk about image quality.
A good body is a like a good tool - it makes it easier to achieve the effect you want.
A good lens makes it possible to even capture it. Perspective, depth of field and sharpness - all that is almost exclusively dictated by how good the glass is and what kind of glass it is.
And since we're talking about lenses. If you buy a camera with a CROP sensor, you should also either be using lenses that are meant for crop sensors(like canons EF-S series) OR use a Speed Booster. A lens built for a full frame camera will basically "waste" light as it will project it onto a larger area that the smaller sensor cannot cover. A speed booster focuses that light onto a smaller area which results in a better SNR.
The last thing I will mention, at least in this post, is that image stabilization has a tremendous impact on low light performance, when hand held, so keep that in mind when choosing either a camera with IBIS or just a lens with a good IS.