The bigger the stump, and the smaller the equipment, the further a person has to start away from the stump in order to get it out. As others have said, a person really needs something small to get in between the root mass to start getting to the stump, so a wide front end loader bucket is hard to work in there. It can do the job, but is also hard on the machine.
Another thing to think about is your enemy the stump itself. A stump is not in the ground like a lot of people think though. A person has to look at it like water on a piece of glass, it is that "suction" that has to be broken in order for the stump to come out. Far more than roots holding it to the earth: it is a root ball after all. Once a person gets under that root ball and starts to pick up, that suction breaks and out comes the stump. Trying to push it out, or drag it out takes a lot of power and traction; it is a combination of lifting the stump up and out that works best. I can only go by my experience here in Maine, but Ash and White Pine are the hardest stumps to remove, while hemlock, spruce and oak are really easy.
As a land clearing contractor by accident, I disagree with renting a mini-excavator though. The cost per day for the production is just not worth it in my opinion; rent a big excavator because it takes sheer weight to get stumps out efficiently. I would never go under a 34,000 pound machine, but honestly, a 80,000 pound class excavator is even better. The cost savings is because of time. While it might take 10 minutes to remove a stump with a 10,000 pound mini excavator at $300 per day, an 80,000 pound excavator will take 30 seconds to do the same thing and cost you $1000 a day. Yes it is 3 times as much in rental cost, but production will be 20 times more! And with an average of 300 stumps per acre (here in Maine anyway), that quickly adds up.
My preferred method, the fastest method, is using a bulldozer to remove stumps, but a lot of rental companies do not allow stump pushing with a dozer as it is hard on the undercarriage, so check first. But it allows the stump to be removed, pushed to the edge of the clearing, and the soil regraded which the excavator cannot do. An excavator/bulldozer combination is best, BUT also means double rental cost, and double transportation cost. Like excavators, bigger is better in land clearing; John Deere 850 or D-8 class here.
I always figure on about 2-3 acres of stump clearing per day for an 8 hour day. A person cannot take the pounding much more than that!