I find alternate picking (the real kind) harder than sweeping. If you listen to Van Halen's Eruption. The middle bit where its the fastest is Tremolo picking, a form of alternate picking. Once people can tremolo pick, they try to do it on alternating strings (what we are talking about). If you crank up the gain reverb, everyting sounds perfect cause you dont need to pick the notes, just touch them. Look at Kerry King, lol. But play on clean and dry up your sound and you will find its a whole mess when actually playing it.

But you never know. To me, alternating picking was the hardest, but maybe your just naturally good at that.