Stannis is harsh, but he isn't by any stretch of the imagination "just." Justice must be tempered with compassion, and applied fairly. Stannis grabs people to burn basically at random because the Red Priestess says she needs a sacrifice and they're 'infidels." He would've killed his nephew purely because he shared his blood and the Red Priestess said she needed it. Stannis lulls himself to sleep at night with the belief he's just, but he's really just a hypocrite, and in his own way just (no pun intended) as poor a choice to rule as any in the Seven Kingdoms. Hell, the Kingdoms would be better off with Tywin Lannister on the throne uncontested. He might place his own family above all, but at least he's not going to kill half or more of the Seven Kingdoms in a holy crusade once he's king (and if you think that isn't exactly what would happen, you haven't been paying attention...it's probably the whole reason Melisandre is with Stannis at all...to convert Westeros to the faith of the Red God).
I've heard Stannis described as "Ned Stark without Compassion" which would be true...if Stannis wasn't a hypocrite who'd kill anyone the Red Priestess tells him to kill if he thought it'd help make him king.
Sorry, I am so not on the Stannis bandwagon. I think some book readers have been so shell-shocked by the books that they start building up the "least undesirable option" in their heads as being less undesirable than they really are. When they said in Season 1 that Stannis would be a terrible king, they were right. I also think some readers identify with the idea of "never getting what their due" and so they sympathize with Stannis' motivations while ignoring the methods he uses to try to achieve his goals. Yeah, he's the "rightful" King if you accepted Robert Baratheon's rule as legitimate...but that doesn't at all mean he's the best man (or woman) for the job.