bumpers are piss poor positions in my opinion: ( if mounted horizontally)
1. the mechanism collects crud and they can be contrary enough as it is with out being coated in mud.
2. I've lost count of how many I have seen bent inadvertently and unknowingly until it was needed.
3. I would suck to have to dig out your hi lift jack or be otherwise unaccessible because it is pinned between a obstacle and the jeep
4. To easy to steal, lose, fall off.
If mounted vertically It is a little better it minimizes some of the above issues and you can keep a eye on it in your mirrors. There are lots of tire carrier mounts for this.
On the hood lets you keep a eye on it, but it can still collect crud, if you like splashing through the puddles. It can be hard on the paint (if that matters) when you lift it up and down It adds weight to the hood or interferes with the opening of the hood depending on how and where it exactly it is mounted.
Mine is mounted across the back inside the rear hatch of my hard top, with a 4x rack. It is kept clean and secure there BUT, I have to open the tire carrier and the hatch to get it, and I have been to places where I could not do that. Which meant I had to wrestle it through the whole jeep to get it. (At least I did not have to dig it out)
The second place I have mounted it on my other jeep is strapped to the long bar of my roll bar (on a scrambler)
The third place is slid under the rear drawer and back seat of my LJ
As for my Flatty, I don't have room for it, I may figure that out where It goes once it is running.
The fact is a hi lift can be a pain to store especially the 60" model but when you need one, you need one.