I'd go with neither. None of them have been out long enough to prove any sort of track record. For me, going with a group that has put out updates and proved they're here is important to me. I bought a DS-X when it first came out and look now, cooll...
I got a DSTT for my girlfriend to try out (I have 2x CycloDS, which I recommend) and it does everything she expects of a Slot-1 card. She doesnt care about extra bullshit like realtime save, custom skins, slow motion, blah blah.
Shes only had a couple games crash on her using a Taiwanese MicroSD card, but it was basically because she was button mashing and the game locked up. Whenever she reloaded after crashing and didnt button mash, it didn't freeze/lock-up. It was definitely good value for what you get, the card is solidly made and its easy to use. It bothers me that you can't sort games alphabetically or otherwise...they are all displayed by when you added a rom to the cartridge (this doesnt bother her in the slightest tho.)
It was the only one I could get for cheap for the time being, and the fast menu speeds were attractive. The only thing that might annoy me is the slight memory card stick out, but I'll just live with it. As for save files, what is the best way to convert them from G6DSR format (.0)? If I remember correctly, R4 .sav files renamed to .SAV work, correct? (I might be getting confused the the DSTT...)
Being pretty sure I'm the first person to post who actually owns both carts, I'm going to give my recommendation to the EDGE hands-down. The interface is so much faster and more responsive than the DSTT's, and the different view modes allow it to suit anyone's taste.
The only things the DSTT has over the EDGE is skinning (since the EDGE's skin support is currently broken), and a spring-loaded MicroSD slot (if thats your preference).