Basically, when it comes to flashcarts, they ALL drain the battery faster. It's because of the special chips in the flashcart and the microSD, both take extra power beyond what a normal DS cart uses. SDHC microSD's use even more power than non-SDHC ones.
WiFi modes also drain power quite a bit quicker regardless of whether you're using a flashcart or not. Volume levels make a big difference too, as well as the brightness setting.
I don't know if any other carts have implemented a power saver mode like the CycloDS has, but in the Cyclo, power saver is mostly for saving more power in standby, supposedly bringing the standby time MUCH closer to regular DS cart levels. I never tested that though. It also helps during gameplay, but only adds maybe 1-3 hours more game time, depending on the game being played.
All I do know is that the CycloDS drains the battery faster than the original R4 ever did, even with the new power saver mode.
As for the DSTT.....well, I'm not sure what all features it has, but I'm guessing it uses less power than a CycloDS (Cyclo's are power hungry bastards), but probably more than an old R4 if you're using SDHC cards in it. (R4 and CycloDS are the only two slot1 carts I have personal experience with)
So yeah, it's pretty normal for a flashcart to munch on the battery. Best thing you could do is to buy an extra capacity battery from DealExtreme. A 1600mah or 2000mah will help immensely. An original DSlite battery is 1000mah.