The Tactical Woven (TW) and Military Grade (MG) cases are of two different classes: ultra-thin, and protective. I’d suggest choosing whichever best meets your needs, regardless of price. Here are a few thoughts on both:
The TW is a super minimal case which is designed to provide a modicum of protection while feeling as much like a bare phone as possible. Though Pitaka doesn’t make any claims, anecdotally the TW does seem to provide a small amount of drop protection, but its primary function is to prevent scratches and minor dings. If you’ve never dropped your phone, or only do so on the rare occasion, and you also have AppleCare+, the TW might be your perfect case. In my opinion, it really does feel sublime in the hand.
On the other hand, the MG is more akin to “normal” cases that are designed to protect from mid-level drops (say under 2 meters). It has an aramid shell molded over a TPU core which completely encases the phone. It should protect the phone from just about any drop in normal circumstances (not talking about rock climbing, etc). Naturally, with the extra protection comes extra bulk, which makes the phone feel wider, deeper, and heavier (the MG is nearly twice as heavy as the TW). If you frequently drop your phone the MG would be a better choice, but you’ll lose that case-less feel of the TW which can be so appealing to some.
Regarding grip, the TW has better grip than the MG. It also shows less fingerprints and smudges. You can feel the texture of the aramid through the finish on the TW, whereas the MG is more heavily coated with a smooth finish that is more slippery while also showing more fingerprints.
One other difference is that the TW provides better access to the camera control than the MG.
That’s my two cents, I’m sure others will have opposing opinions.