The first principle of guitar sound is understanding that the strings are THE most important part of the instrument. They may not have the sex appeal of a new set op pickups, but really, the guitar is entirely built around the strings. Every part of the guitar is designed to support the string's job of vibrating in ways that are controled by the player. 'Kinda puts a whole new light on that little five-buck package!
So, as you said, the heavier gauge strings helped to 'fatten up' the sound of your old axe. You don't get any sound out of an electric guitar unless there is a vibrating magnetic mass within the field of your pickups. More mass = more sound. A heavier string usually produces more of the fundamental note, with fewer harmonics, than a thinner string at the same pitch. This also makes it sound 'fatter'.
Your friend's guitar, with the thinner strings on it, is probably easier to play than yours, but I bet it sounds a bit 'thin'. (By the way, congratulations on your new axe; I happen to be a Washburn fan myself.)
Stevie Ray Vaughn got a lot of his killer tone from his heavy strings. A set of .011 GHS Boomers can feel like a half-dozen coat hangers to someone who's used to those .009 'spider webs'!
As with just about everything else, it comes down to the music you play. If your sound is mostly based on the effects and the amplifier settings you use, then the strings become less important. Thin strings make deep bends and dive-bombing, whammy-bar zoomies playable. If the guitar itself is the major part of your sound, you may want to stay with .010 strings, or even try a set of .011's for a while.
Try playing a guitar on its own, without an amp. If it sounds good like that, it will sound even better plugged in. If it does'nt give good tone on its own, plugging in will just make it louder.
Whatever you choose, keep 'em CLEAN! A fresh set of strings has a clear, rich sound that gradually gets muted as oil from your fingers traps dirt in the wound strings and causes corrosion in the plain ones.