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Sensor size has so little bearing on image quality/camera capabilities that it's not worth focusing on.
For example, my Nikon D3000 has the "DX format" (APS-C) sized sensor, which is 2/3 the size of a standard 35mm or "full frame" sensor. It performs just as well as its bigger-sensor compatriots, though, for one simple reason: Sensor quality, not size, is what matters.
Point-and-shoots give you poorer-quality images because they're generally made far more cheaply, and with much lower quality glass between your subject and the lower-quality sensors they're fitted with. Many of them have APS-C-sized sensors in them, yet still perform poorly.
What matters at low light is aperture size -- a larger aperture gets more light through your glass and onto the sensor. (Also a longer shutter time gets more light, but risks adding motion blur if your subject and/or your camera are moving.)
Like Z says, the quality of your glass is your real deciding factor once you get into the world of quality camera bodies (i.e. anything above point-and-shoots). And the big names -- Nikon, Canon, Sony -- all have quality glass (Nikon and Canon beat out Sony, but not to any degree anyone short of a high-grade professional would ever notice).
Anyway, both of those cameras are good. I also recommend the Nikon D3000 -- it's a bit older now, which means it can be had more cheaply, but it's just as good. Really the only thing it lacks is an HDR mode, which is great for high-contrast images, but isn't really necessary. The nice thing about getting one of these bodies is that it doesn't matter how old (or new!) the body is, a Nikon lens will fit a Nikon body. (For best results, make sure it's designed for the sensor format (size) that you have, but mis-matched lenses/sensors won't do any harm -- just means some of the light coming through the lens misses the sensor (lens for larger-format sensor), or the sensor only catches a subset of what comes through the lens (lens for smaller-format sensor).)
DSLRs are great, and the compact mirrorless cameras like that Sony are almost as good -- plus they're more compact. Personally I like the familiar feel of the DSLR (it's just like the old SLRs I used to use back in the good ol' days of real film); the compact mirrorless cameras feel like the cheap point-and-shoots I've used since then. Both take great pics, which type you go with is purely a personal preference thing.