It's an interesting question, so let me answer it from my point of view and why I like 79 twinking.
First of all I like normal wotlk pvp. The pvp you could have at lvl 80. I don't like having half of my default class skills. The more skills you got the more plays you can come up with, just like on 80. Then why 79? Well, because of quickly becaming competetive. I also do have an 80 lvl pvp toon, but even though I've spent a lot of time on it doing arenas, raids etc I'm still far from being BiS and I can't just fight everyone on equal level, because of gear differences (either they got weaker or stronger gear than me). On 79 you can just craft your set, do few dungeons and voila, if you're good you can beat anyone. Ofc you can also get yourself some tbc items from raids and that can take some time to get, but these are rather minor changes, they don't make such difference as on lvl 80.
In addition bgs are my thing. I really love playing bgs. And I mean competetive play. The level on which 80 lvl bgs are played is total garbage. People have absolutely no idea what to do or they just don't care. You feel like 80% of your team is played by monkeys. Maybe if warmane added ranked bgs things would change, but for now it's just a mere wish. On 70-79 bgs are much more competetive. Significat portion of the 70-79 twinks play on this bracket only, which means they play bgs all the time, often for years already. They know much more about playing bgs and objectives than most of the 80s. And because of that bgs are played on a whole different level.
Also, the difference in making builds. What's the bis item for arms on 80? Smourne, duh, right? What's the bis for arms on 79? Well, many players would argue here because the answer is not that simple. There are many weapons that are equally good, it's up to you to decide which suits your gameplay best. Same goes for every other item. There are even items from vanilla content that can be your BiS on 79 and that's quite interesting. People experiments with items and you can see many different approaches to every class.
The balance of classes is also different on 79. Some might like it how it is there, others prefer how it is on 80. As for me... I like both to be honest. But since my favourite class is much more viable on 79... I play 79 :P
Btw. Thorbjorn, are you a twink? I think I've seen you write in some threads regarding twinking, but not on the toxicfest 79 thread, any other bracket perhaps? xd