It does. With more cells, you'll have higher voltage and the energy will be higher too. With the 1300mAh battery you can only draw 58,5A which is not enough. According to my calculations, the coils can draw over 60A. The other 3000mAh battery can supply 120A which is a lot safer and the battery will also last longer.
Thanks :) I agree that making it wireless would be a lot more interesting. Good luck if you decide to build one :)
I got them from hobbyking.com They have a ton of batteries.
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I'd suggest checking the update schematic on https://www.instructables.com/id/Coilgun-1/The MOSFET can handle 110A continuously and 390A as pulse current so that isn't going to be a problem. The only real limitation is the battery. The ones I'm using can handle about 90A.