How do you know the Hobbs switch is broken? Do not use your nitrous system without that switch properly hooked up! Seriously, you could ruin your motor. When I was had the stock 5.0 under my hood...& I was young and dumb...I was having trouble getting my nitrous system to work properly. It would work for a second then shut off, or sputter. So I stupidly unhooked the Hobbs safety switch. I went to the track a few weeks later and began melting spark plug tips! I mis shifted once with the nitrous on and blew a 6ft. flame out of one of my tailpipes! Fast & the Furious style...no joke!
You can get a new switch at your local speed shop. Who installed this system for you? Or did you? If you had it installed by someone that knew anything about dry nitrous systems on fuel injected cars they should have known how important the Hobbs switch is and that it must be connected and working properly to assure the safety of your motor. Did you say there is a larger than stock fuel pump in that car? That's strange though because even the stock fuel pump flows enough volume & pressure so that the system should work fine. That's the key to a safe nitrous system...making sure that your fuel system flows enough volume to hold the boosted fuel pressure up to around 80+psi. for an entire 1/4 mile run. When I had a 100hp shot of nitrous my 155lph intank pump was sufficient. But when I stepped up to the 150hp shot...that's when the Hobbs switch began cutting off the nitrous flow because I didn't have enough fuel volume. So now I run a MSD inline pump that flows about 200gph (I think??...it's been a while). I still don't understand why your new Mustang with all the mods it has on it doesn't feel as fast as your old stang?! Or did you mean just when using the nitrous on the 2 cars? Did you even use the nitrous system on the other one? Sorry for all the questions. Just trying to get a feel for what exactly is going on here. Give me some more details and we'll figure this bug out. About the popping...did you ever change your fuel filter?