Doesn't matter. Either will be good for you and whilst you may have had a problem with a single lithium battery it is not reflective of Nikon, in the same way that issue is likely to affect Canon at the same rate. A $24 lithium battery is cheap anyway... I have one that cost me $100... was it from eBay or some third party Chinese non brand? Blame the battery not the camera I think.
Taking clear shots is more than the camera body if that at all - these bodies will give you pretty much the same thing overall. The obvious 14Mp v 12Mp isn't worth worrying about either. But I do know the D3100 overall is a good unit for starting and if you end up with any kit lenses, try and get yourself at least one fast prime, such as (Nikon wise) 35mm f/1.8G DX or 50mm f/1.8G. I recommend the Nikon on the basis it has good lens options available for you as a starter.
