For any serious stump removal an excavator is the way to go. But, I've removed hardwood stumps, up to about twelve inches in diameter, with a Woods 1050 on a John Deere 6400. The soil condition and species of tree stump have a lot to do with how large a stump your tractor/backhoe will remove. If the stumps are large, say two feet or more, and the soil covers large boulders, or even ledge, you need at least a 15ton excavator, with a rugged thumb, to successfully break the large roots and lift/pull the stump out of the ground. The alternative is to dig down to the roots and cut them off with a saw or axe, before you try to move the stump.
The first time you tackle a big old maple stump, with a large tap root, you'll wish you had rented an even larger excavator. Twenty tons, or larger, is reasonable. If the stump is fresh cut, you'll be amazed at how heavy it is. Once you have it out of the ground, the excavator, with hydraulic thumb, will prove a lot more useful than a dozer, at loading the stump onto a trailer, or into a dump truck.
There are several stumps, around the farm, that need to come out, and I'm planning ahead, so that I don't waste expensive equipment rental time. I have an old Cat D4 and have used it to move stumps, but i quickly tired of trying to dig stumps out with it. So, i'm looking forward to a weekend using a 20 ton excavator.
Enjoy the stump pulling. It is a whole lot easier, and safer, if you have fun doing it.
Sparky