Well, my TARDIS is awaiting parts and is off-line due to COVID and the chip shortage, so I cannot jump back 10 years to compare.
But in 2022, I can say the 1100T does not compete. It has more cores than the i7, but no hyperthreading. The 1100T also has a smaller L3 cache (6MB vs 8MB) compared with the i7.
As for the two Intels, the Xeon may be a little bit faster
on paper (and some benchmarks), but I highly doubt any differences would be noticeable to the "blind" naked eye. There are just too many other factors affecting over all performance, to include the RAM, drive and the graphics solution, not to mention the program(s) you are running. By "blind", I mean if you were evaluating only with your own human senses, one processor at a time, and you had no clue which processor you were using.
While the OS can take advantage of multiple cores, not all programs do - and you didn't tell us what this computer will be used for. I note the i7 offers significantly better single-core performance.
There are several sites that compare, but I think between the two Intels, this site sums it up pretty well:
HW Bench - Intel Xeon E3-1290 v2 vs Intel Core i7-3770.
Gaming - No clear winner declared
Productivity - No clear winner declared
So, first, if me, I would go for a modern platform and current processor that supports the latest operating systems, security and applications/programs. But if I was forced to use such legacy hardware, and my choices were only between those two Intels, I definitely would go with the i7, unless the used price for the Xeon was just too good to pass up AND it came with a decent warranty!
Ideally, the 3770K should be the chip to get, with a good cooler.
I agree - and with a decent graphics card, a big chunk of RAM, SSD, and of course, a quality PSU.