So lately I've been trying to play the solo in Dream Theater - Never Enough (off the new album). Not the crazy sweep picking part, but the easier sounding part before that (starts at 3:45). And it's a struggle, so I've been working it up through the tempos really slowly starting around 60, and I can get it up to almost 80 without much trouble (but I think it's played around 136 or something). One big issue at the moment is hand synchronization and getting the fingers on the string and off the string fast enough to avoid the "thunk" noise when you miss.

Anyway, for the sake of learning technique, should I be doing exercises like 1-2-3-4 4-3-2-1 all over the place, or trying to learn songs that are over my head? Which one is more beneficial and how did you do it?
im currentlty in a similar boat ad i find a mix of exercises and song work best for me, but i would say dont try songs that are over your head because youll just get dissapointed find a solo at your level and work on getting in perfect.
What the ancients called a clever fighter is one who not only wins, but excels in winning with ease.

Sun Tsu, The Art OF War
Well, I usually just learn hard songs which give me ideas about how to play better. But exercises are solidly worth it, definitely. I really should do more of them. Basically, do songs and exercises.