IMO, you really want the Vanguard Veterans box. I don't know the relative ages of the two kits, but they're both much more modern than either of the vanilla Terminator squads.
The reason I'd lean toward the Vanguard Veterans are, well, they're Vanguard Veterans, and Deathwatch can't take the basic Assault squad. There's nothing stopping you from using the standard Assault squad AS Vanguard Veterans of course, but as others have said the armour of the Assault squad is quite plain in comparison.
Also, unless I'm reading the datasheets wrong, Vanguard Veterans can't use the Eviscerator, the Combat Shield or the Flamers in the Assault squad box.
Finally, I haven't actually built the current Assault squad, but the legs look very short to me, even for Firstborn. It might just be the pictures on the GW website, but to me the Vanguard Veterans look better proportioned.