if im fighting with people who have better gear the the monster it usually goes faster online. But if everyone has decent gear i can usually down the monster faster by myself solo. Not to sound like an ass or anything but the fights offline shouldn't drag on at all. Try experimenting with different weapon types, elements, etc...
Depends some of the monster are absolute b*****s online compared to offline for example Gobul is ridiculous underwater online while offline he's average. Also some of the monsters are harder with more people trying to kill it Lagi online constantly spams that stupid electrical charge attack or roars to temporarily paralyze you and then does it's Pikachu like thunder shock. Lagi Offline is much easier, only starts doing electrical charges when it starting to get dangerously weak.
"THE PRESIDENT HAS BEEN KIDNAPPED BY NINJAS. ARE YOU A BAD ENOUGH DUDE TO RESCUE THE PRESIDENT ?"
I've had Lagi do his electrical charge pretty close to the beginning of the fight offline too... I mean, he spams it as his health gets lower (which really just gives you an opening to bring on some serious pain if you're smart enough to dodge it, in fact, I wish he'd use it more).
Online, so long as you have a competent team, I find the monsters to overall be easier. Soloing them isn't so much harder as it just drags out. I just (mostly) solo'd online Barroth because I DC'd (not entirely solo'd, we got his tail off before everyone DC'd), and really, short of being a lot longer, there isn't much difference between the offline version.
INJECT HEROIN INTO YOUR DICK! THREE MINUTES OF AWESOME!