I'm delighted to hear that you'll be heading to Tanzania. I lived there for two years, and as far as I'm concerned it's the greatest country on earth (despite its lack of zoos, and the fact that it is truly appalling at football).
I'm presuming you'll be based mainly in the 'real' north, but will you head down to Mikumi and Ruaha? If so, the opportunity to head to Udzungwa should not be missed: it's right off the highway, and you've got a great chance of seeing some truly extraordinary primates.
I think your birding fetish will be satisfied, wherever you are. Serengeti may be famed for its herds of zebras and wildebeests, and its lions and cheetahs, but the birds are extraordinary too - and if you have a guide who knows what he's doing on the avian front, so much the better (most of them focus on the glamorous mammals, which is fair enough).
I'll be very interested to hear how you think Tanzania compares to Uganda. I've not been to Uganda (but have been lose to the border, in TZ), but have Ugandan friends. TZ is undoubtedly less economically developed, and a lot sleepier as a country. It is also a great deal more socially conservative, particularly away from the cities (I presume you'll be spending some time in Arusha). Compared to Kenya, it is a wholly different land: the frenetic, energetic, edgy nature of the northern neighbour is largely absent in Tanzania.
My main travel advice for visiting the place: make the effort to learn a little bit of Kiswahili before you go. Just the greetings would be excellent: the number one beef that Tanzanians have with wazungu (foreigners) is that they don't take the time to greet people politely. Just being able to run through a few polite greetings will take you a very long way, with your guide, i restaurants, with people you meet.
I'm looking forward to following your journey!