I'm also thinking the original poster is referring to the tX7 and tX1...those are two currently available models in the T-series lineup. The 'T1' was an oldie - about 5-6 years ago.
Assuming you meant TX1 and TX7, I have the TX1 since December. I can't directly compare to the TX7, but I can verify that the battery life will be a bit better with the TX1, as the TX7 screen has a higher resolution and sucks up a bit more battery life. I would think either one could last a day of shooting though...one convenience of these cameras is the ability to slide the front cover down to turn on and shoot, and slide up to turn off...it makes it easy to shoot with the camera and immediately turn it off to conserve battery, and when ready to shoot again, slide the cover back down - it's started up and ready in under a second.
I have been happy with the little cam - couldn't be more convenient to carry, solid as a rock, the touch screen is quite nice in use, and actually shockingly better than buttons and dials as far as camera settings and changes (I'm a DSLR shooter and like to choose manipulate many of my own settings). The low light capability of the camera is downright remarkable - using hand-held twilight and anti-motion blur modes, one can shoot handheld at night outside and get crystal clear shots with great detail and low noise. Daylight pics are OK - nothing super-special, nothing bad either - typical compact camera fare (using a DSLR, I'm not much impressed with ANY compact camera shots - but they all do just fine for basic snapshots and prints).
The TX7 has a few advantages - nicer LCD screen resolution, built-in HDR mode, wider angle lens (24mm vs 35mm).
The TX1 has a few advantages - physically a smaller camera, better battery life, ability to purchase an 'infolithium' battery which reads out remaining battery life in minutes rather than a little bar graph.
Feelf ree to browse my gallery of shots taken with the TX1:
http://www.pbase.com/zackiedawg/sony_tx1
I have only had it for 1/2 a year, so not too many shots yet - I mainly use it as a backup to my DSLR when I don't feel like carrying the whole kit.