I like most here have both also. I happen to like the mechanical trigger. I have an early Win. 101 in 20ga. that has a mechanical trigger. Most of the others have inertia triggers. I've never had a problem with either, but it is true about the inertia trigger that if you have a dud, or a blopper in the first shot, you will not get the second shot.
As far as using snap caps in an inertia gun, just tap hard on the butt stock and it will set up the second trigger. Whether it is important to release tension off the triggers or leave them cocked, would probably fill a small book.

David