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Tough choice if it were me. I would want to consider how many miles were on the truck, and how long I expected to be driving it. Also would have to consider the shops doing the install. Jasper reputation has been spotty, for engines anyway, not sure about trannys. I think the Ford rebuild warranty is pretty good, and you won't have to hope for good will from the installer. The dealer will probably treat you right.
I guess if I planned to keep her, I would go with the Ford.
If you decide to go with Ford, just be sure that they are actually installing a Ford rebuilt, not a Jasper! I have been told that Jasper is supplying a lot of OEM's with rebuilt components these days. That having been said, I have used Jasper rebult transmissions, and not had any problems with them. Jasper does insist on a new cooler or cleaning the existing cooler with their 'certified' flush unit.
I would buy a used trans out of a late 05 or a 06 that got smashed. Low mileage units can be had for $1000-1300. Other than the problems with early 05, they are strong.
Keep in mind that since your case is cracked you will likely have to pay for the core on a rebuilt trans.
Also, you can buy a brand new case for around $600 and the new snap ring for $50 and rebuild yours which only needs a new case. With labor you you should be well under $2500. You can save more if you can handle swapping the trans.
Between the two I would opt for a Jasper. Having two Ford remans in Explorers over the years I saw they are nothing special. You often get a better trans from a good local trans shop with updates installed for less money than a Ford reman trans.