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I played with an A4988 and also with an Easy Driver (not the "Big" version) when motorising my focuser. One thing to note is the amperage you can push through the boards without active cooling. I think that might be about 1A with the A4988. The big easy driver you've linked there says it should be able to do 1.4-1.7 without active cooling, but needs cooling when approaching 2A.
The bigger motor you've linked to is rated at 1.68A. That doesn't mean you have to run it at that, but it's where you'll get the most torque, but it's also the max recommended. Based on that I'd be inclined to get the Big Easy if you go with the larger motor, either if you go with the smaller motor. The bigger motor has about twice as much torque, and can chew up about 5x more power. Without knowing how much torque you need it's difficult to make a recommendation.
One thing to note is that the bigger motor has 0.9 deg per step, whereas the smaller one was a more typical 1.8. I don't know the sort of resolution you need, and you can increase this by microstepping, but you lose torque and I believe increase the chances of misstepping.
I'm not being all that helpful, I know, but if there's one take-away from this: pairing the A4988 with the bigger motor might not make for the simplest of solutions.
Oh and here's a tip I learned playing with this stuff: never, ever disconnect the motor while there's power going to the controller board. You'll instantly brick the board. I did this more than once due to having dodgy connections whilst prototyping. Just to be sure, I'd recommend buying a couple of controller boards.
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