In terms of just overall prestige, there's no question that the IWGP Tag Team Championship is well above that of the TNA World Tag Team Championship, at least in my view. For those that aren't very familiar with Japanese wrestling and Japanese wrestling companies, which is probably a good sized majority of America's wrestling fans, they'd no doubt say the TNA tag titles.
For the most part, the IWGP titles in TNA have been pretty much a joke in my opinion. I don't have any real interest in them and having the British Invasion win the titles and sit on them for nearly four months certainly didn't kindle interest in them. I sort of feel the same about Scott Steiner and Booker T's reign as TNA tag champs. For the most part, they just sat on the titles.
Stories are out that New Japan Pro Wrestling isn't all that fond of what TNA's been doing with their titles. One reason why they agreed to this relationship is because of the Dudleyz. The Dudleyz are pretty over in Japan and New Japan wasn't happy when TNA had them drop the titles to the BI, a reign that New Japan didn't even recognize as official until a month into it. Supposedly, most of New Japan's audience still believed the Dudleyz have been the IWGP champs this whole time. TNA having the Dudleyz take the IWGP titles back, giving them a total of 23 world tag titles, is probably just to keep New Japan happy.
Personally, I'd rather TNA sent the IWGP titles back. Counting those titles, TNA currently has 7 different championships on their roster. That's the same as the WWE only TNA has about a third of their air time. Also, if TNA is mostly going to have the Dudleyz sit on the IWGP titles as the BI did and have the BI sit on the TNA tag titles as Booker and Steiner did, then the whole thing's just a waste of time in my opinion.