I see it as a trade off. If you only need one kind of battery for your gizmos, keeping them fed is easier. If you have battery diversity, you might find it easier to find a battery that will work for one of your flashlights. You also may find that different battery form factors work better for different purposes.

I have no hands-on with the MP7 but I do not care for the 3xAAA form factor. You get less power than you would with other form factors (such as 2xAA or 1xCR123A) and they're more fiddly to change batteries.

For me, I would in almost every circumstance for EDC and emergency use recommend an LED. After that, most non-flashaholics are better off with AA-powered lights. Flashaholics will often want CR123A or 18650 or 14400 or
10440 or some other kind of oddball cell. When you've figured those things out, output, runtime and whether you need variable output and disco modes should help you narrow the field.