Welcome to the forum, Loose Cannon.
The JB/Hot Rails combo is a standard; I would say that they are a very close sonic match; the Hot Rails will be be more 'point specific' since it's sampling the string strings from a much closer distance than the poles in a full sized humbucker, tho.
the hot rails and the invader sound nothing alike to me...i have had both...still have the hot rails, sold the 3 invaders i had. the hot rails while still thick has more of an edge to it and much more clarity and articulation than the invader. also a jb jr/hotrails combo is nice...i have the reverse of that in a strat...jb jr bridge, hot rails neck and it works great for me.
Hot rails neck is THE superior single coil-sized bucker for the neck. I like the DiMarzio Fast Track 2 best for bridge. But the thing about the hot rails is that they're unparalleled in terms of full size buckers. I don't really like the JB Jr period, it's way too single coilish sounding and it is.... just lacking something. Something big.
My strat. Sounds awesome, though a Super Distortion may sound a TAD better for metal. The Fast Track 2 can still pull off (sorta) the classic strat sound though, and it looks normal since it's small, and that's why I use it.