I'm fully committed to the Integra 6MT, but the Accord 2.0T was one of my frontrunners for a while and I'll share some of my thoughts:
New vs Used: Being the first to own something is exciting, and I frankly wouldn't want to be the second owner of a "fun car" like a Si (ok, so I bought a used Si once and had no issues) or a Type R, but a Certified 2.0T would be a better buy than a new one, in my opinion. The Certified warranty is GREAT. In a perfect world, you could even get a gently used Certified 2.0T for significantly less than one brand new... but we all know how things are now.
6MT vs Auto: Simply put, I wouldn't get the Accord with the 6MT. The reviews are pretty much unanimous in the shifter feeling loose and disconnected, and the manual transmission seems to hold the 2.0T back in performance (at least on a straight line). The 2.0T automatic transmission is great, and it eliminates the need for the LSD. If I'm going to do the shifting work, I want it to feel good, engaging, and worthwhile. The new Si gets rave reviews for its gearbox, and that means a lot for just about anyone who wants a manual.
Power: The Accord 2.0T lacks the track look and some of the capabilities you get with the Type R, but good luck finding this kind of power in something else for the price. I don't expect that I'll be able to make my Integra as quick as the 2.0T, and would hesitate to try knowing the 2.0T would put out well over 300hp for the same/less money.
Design: Fully stock the 2.0T is... not the worst thing that I've seen, but certainly not exciting. The interior features (minus the stereo) are comparable to the higher-end Integra models, but it's big. There's a strong community that's building on this car and a lot of low-cost ways to make it look and feel more exciting. That said, there are a lot of people out there ruining these cars in a lot of low-cost ways--the difference between a medicine and a poison is often the dose. With a little work, these can fit right in at car meets... but with no work at all, it can blend right into a nursing home parking lot.
Room/Practicality: The 2.0T is a larger vehicle altogether, and while I haven't sat in the Integra, a lack of room/comfort hasn't been an issue I've seen reviewers mention with any of the latest Hondas. The Integra roofline limits its back seat headroom vs the 2.0T, but I'll have a toddler back there and not Shaq. The usability of that hatch is worth the limited headroom, in my opinion.
Overall... the 6MT Integra and the 2.0T are very similarly priced, but the Integra is more stylish and should be a lot more fun to drive and throw around, even if it's not as fast. If the 2.0T had an engaging 6MT, it might be a coin toss between the two for me.