For lower noise in low light, the 6D is the clear upgrade. Moving from a T2i to another APS-C body like the 7D or 70D won’t give a major low-light improvement; the 7D is especially similar to the T2i in that regard. A full-frame body like the 6D typically gives about 1–2 stops better high-ISO performance.

It also changes your field of view: your 50mm on full frame will feel noticeably wider than it does on the T2i, which may solve your “too tight indoors” problem by itself.

Be careful with the 24-70mm f/2.8 idea for low light: compared with your 50mm f/1.4, f/2.8 loses about 2 stops of light. It’s a great, versatile zoom, but it won’t beat your current prime for dim venues.

So if your main goal is cleaner low-light images, choose the 6D first. If your main issue is that 50mm is too tight, consider a wider fast prime instead of relying on an f/2.8 zoom. Also note that EF-S lenses won’t work on the 6D.