True blood vamps are faster and some of them can fly. Plus they have some ridiculous healing feats. But they're still susceptible to stakes and sunlight and all the weaknesses of historical vampires.
Twivamps aren't as fast but they do seem stronger. Plus Meyer completely ruined the vampire genre by making the twivamps into sparkly superhero emo-types, complete with their own set of mental superpowers. Add that they're immune to sunlight and pretty much any other weakness of vamps, and they're a lot harder to kill than the trueblood vamps.
So yeah, twivamps might take some time chasing down the true blood vamps, but they'll eventually win.
That's ok though. True Blood the show is way better than the Twilight movies.
Physically, I doubt the Twivamps would be able to catch them. But that's not to say Jane can't cripple them with her pain projection. Or that they can't hunt them during the day. Etc.
True Blood has a total of 6 vampires that would be physically on par with the Twilight vamps. And of those, only 2 have exotic abilities which would be a challenge to the supernatural gifts that a number of Twivamps have. And none of these 6 vamps have anywhere near the durability of a Twivamp.
Apart from that, the average Twivamp is a good deal stronger, has virtually no exploitable weaknesses, and is much more durable than the average TB-vamp.
That version of Bill was quite strong. But his TK was nowhere near as powerful as Benjamin's (Benjamin was pretty much The Avatar...control over all 4 elements).
Russell is very strong. But I do not remember any of the True Blood vamps having strength on par with even some of the weaker vampires (such as Edward).
The vampires that can fly will be taken out of the sky by Jane: her part darts shoot fairly quickly and they are invisible to all except Bella (maybe someone else but she was the only one who demonstrated the ability to see Jane's and Alec's special powers).
IIRC, Russell and Bill (Billith) are faster than any Twivamp. Other than those two, none of them come close to even just regular vamps.
Benjamin's ability seemed to be elemental control at best, instead of actual tk as seen with Bilith. And Bilith's tk was capable of creating tremors in the earth, so it's not far off.
According to TB-powerscaling, Warlow, Godric and Salome are on that level as well. But as far as speed is concerned, iirc twivamps on average are as fast as the average TB-vamp.
It's the strength and durability which gives them the edge. I'd say the average twivamp is as strong as a super-ancient TB vamp like Russell or Warlow. And we have dozens of such vamps against dozens of the much weaker TB-vamps.
Not to mention that a large portion of the twivamps have exotic abilities(shielding, telepathy, precognition, electrocution, sensory deprivation etc), as opposed to only 2 such TB vamps(Warlow's fae abilities and Bilith's tk/precog). Bilith and Warlow would make this hard to win, but at the end of the day Twivamps stomp.