Well, front brake alone almost always stops you faster... now if you're saying that using the rear brake alone on your new bike is stopping you faster than both brakes on your old one, then that's not bad.

Walmart bikes (and I can only imagine what you've been riding) are probably not the best things to use for something like commuting, where reliability is key. Frames and components will both be subpar, for the most part.

Congrats on the purchase