15 inch speakers do a couple of things:
one, they tend to provide more low end and lower mids at the same tone settings, that allows more harmonics to come though if you back off the bass knob til you get the same amount of bass as a 12... if you are playing through a relatively full range guitar friendly 15 inch speaker. Makes for a richer, fuller sounding lead tone if you have the right 15 inch speaker. If the amp isn't working as hard for a given volume setting pushing high wattage demanding low note sound waves through the system there will be less mud in the tone at high volume settings. Blues tones sound particularly nice through one or two 15's.
two, they tend to be more efficient watt for watt volume wise,
three, if you hit a low droning note and simultaneously hit a couple high ones on a cheaply made 15 it will sound like muddy crap, the same thing will not drastically effect a 12, think the more massive 15 inch cone is at fault. The EV 15l will not be plagued by this problem, Cast frame speakers with large maghnets tend to not be as affected.
four, the 15 inch speakers will project their sounds further away from the cone than a 10 or 12. If you put yourself 20-30 feet back from a 15 cab and a 12 cab side by side you should hear a pretty good difference, especially in a crowded room.
Some 15 inch speakers were designed to work for lead guitar. Some work by accident. Hope this helps.