There aren’t too many differences functionally. They both have generally weak IR illuminators (although the A3 beam can be focused, a feature that’s locked out on the PEQ-15C), IR lasers are on the weaker side, but not horrible, and the vis lasers are comparable to just about any other vis laser on the market. A3 is green, PEQ-15C only with red. Neither are useful in brightly lit conditions beyond 10-15y, although the green A3 does seem a bit better.
Obviously the A3 has an all aluminum body, PEQ is polymer. Both utilize a single CR123. A3 comes with a QD lever Mount, PEQ is a standard flathead screw mount. A3 sits a bit taller than the PEQ. There have been reports of the A3 draining batteries with the switch in the off position, but that seems to have largely been fixed.
If it were my money and those were my only two options, I’d go PEQ. I like the controls better, performance is very similar between the models, and I have more trust in it’s durability (even though neither are absolutely bulletproof). Factor in that you can get the PEQ for less than $1k and presumably the A3 is going to be $1.2k-$1.3k and I think the choice is pretty easy.