He's exactly what they hate about Hope: whiny. He's a ball of negativity. He looks depressingly at things and says stuff like, "I'm too old for this", and anything equivalent to "I'm unhappy about what's going on". The difference is that his weak personality is deliberately underwhelming (unlike Hope who wants to kill your teammate), so people don't feel like they're being forced to like something they don't. They think, "it's too obvious to dislike Sazh, so I'm gonna' go against the grain and like him." That's very unique, guys.
Sazh sucks. He sucks big time. He's dog poop excreted at an angle over a downward street, shooting toward traffic with unrelenting crappiness. He usually acts sad -- thoughtlessly sad, says nothing meaningful -- and on occasion will come out with kind of a, "whoa, let's think about this!" type one-liner. I think in those (few) moments, the takeaway is supposed to be that he's a middle-of-the-road kind of guy, despite his pervasive whininess and his inability to present the viewer with a compelling outlook at these times -- and there's his unconvincingly dramatic outburst at Vanille, which I must mention because holy hell that scene sucked.
Sazh is a suckhat. A suckhat who wears a hat, which was given to him by his fanbase, not realizing that it's unfashionable and doesn't suit him. It's an ugly and useless hat picked out by ruffians and vagrants, and it's intended for what the ruffians and vagrants, who habitually worship their own feces and compliment each other based on the physical attributes of their feces. "Oh," one exclaims, before continuing his speech the way he thinks noblemen do in this day and age, "'tis mine honor to beholdeth thine poop, for 'tis of foul odor!" "Indeedeth!" replies the other. "I hath poopethed it mineself!"
EDIT: To continue a thought, the hat is intended for what ruffians and vagrants consider to be a respectable man. Given what we know about those ruffians and vagrants, it is probably less a respectable man and more a bad character like Sazh. And so for that matter the hat suits him well -- except it came with a letter that said, "this hat goes to realistic, middle-of-the-road kind of guys that stand out from the usual ridiculousness of video game characters", and that definitely doesn't fit because Sazh is ridiculous, not middle-of-the-road, not realistic, and his fans are totally full of it.