In the last 4 years I have removed over 1000 stumps at my lot.
I own a Ford 575D backhoe, a CAT D6C Dozer (15 ton), and a CAT 225 (25 ton) excavator.
I used all of them to pull stumps, however, the soil type, tree species and stump size has a lot to do with which machine to use.
Any evergreen tree in sandy soil, no matter how big in diameter, is really easy for a dozer to just pull up to and lever it out of the ground with the blade raised.
Yet, the same dozer with a 12" diameter Maple tree in soil with more clay, will not come out as easy, and you beat the **** out of the machine. It's better to use a backhoe, or an excavator...
An excavator is definitely easier to maneuver around the stump that a backhoe is. I'd recommend an excavator no smaller than say A cat 305.
Again, depending on the soil & tree species, the dirt ball that accompanies the stump is another issue. A cat 305 may be able to dig around the stump and shimmy it out of the hole with a ramp, but unlikely to just be able to pick it up with the bucket & thumb, and drop it, if it's a sizeable stump with a large root ball, and heavy clay-type soil.
I had some 24" - 28" diameter silver maple stumps which were about 8 ft in total height with a root ball that was 8-10 ft in diameter, some of those weigh in excess of 20,000 lbs. My CAT 225 with manual thumb could not pick them up, as that machine can only lift 16,000 lbs close in.
You may need to ask at a rental place in your area, tell them soil type & tree species type, and see what they recommend.