Re-Gearing after a substantial tire change is one of the best investments you can make. BUT, make it worth it because re-gearing and axle work in general isn't very cheap. It's labor intensive, and if you're asking this question it's probably best to have a shop do the work for you. Expect to pay at least $150 to have a rear ring and pinion set up by a shop.
The best bet is to find out what ratio you currently have in your truck.
Post that here.
Then tell us if your Edge has a 3L or 4L engine.
I'll argue that a jump from 3.73 to 4.10 is not worth it, financially. A jump from 3.73 to 4.30 or 4.56 would justify the cost to me.
And while you're in there, ask yourself if you want to much wheelin' with this truck. Re-Gearing offers the perfect opportunity to add a locker or a limited slip. You won't have to pay the shop much (if any) extra labor charges to swap an open carrier to something more off road friendly (like a locker).
1999 Ranger 4.0 Sport --SOLD!--
2009 F250 XLT CrewCab ShortBed
5.4L / 6 Speed / 4.10LS