Odium has killed Shardholders and destroyed other Shards before, in times before the current story in the Stormlight Archive, something Ruin had yet to do (although he did try during the events of Mistborn).
The letter that takes up some of the epigraphs in The Way of Kings - the one implied to be from Hoid - makes clear that Odium paid visit to Sel, the world on which Elantris takes place. According to Arcanum Unbounded, this happened in Sel's prehistory, long before any story set on that world, and all we see are the results. The two Shardholders on that world are dead by Odium's hand, and the Shards that they held were destroyed thoroughly enough that their power could not be picked up by another. It is possible that this is not the only world or gods he has done this to - Tanavast as Honor's Shardholder certainly is dead as per the end of Way of Kings although what the full story is we still don't know.
From the perspective of a Shardholder (Honor), this makes Odium a rather ultimate evil, as Shardholders have been proven to be somewhat eternal. They've created worlds, and will last beyond those worlds, and all the humans on them. Unless this one thing that has just as much power comes along and rips it all apart.
Ruin, by contrast, only attempted to destroy Preservation after Preservation betrayed and imprisoned him.
Weighed into this is the potential for Odium to outmaneuver those that would oppose its murderous plans. While it has the same power as other Shards, some Shards have shown varying ability to peer into the future and plan accordingly. Vorinism, the main religion seen in Stormlight Archive, teaches that this futuresight is of the Voidbringers, of Odium, although their mythology is shown to get several things wrong, and may simply be an artifact of Honor not having this skill. More worryingly, perhaps, mention is made of a Parshendi shape called "nightform" that can be seers, and predicts the rise of Odium again. Many Parshendi forms appear to have nothing to do with Odium, but this does appear to associate Odium with futuresight and mark him as far more dangerous than Ruin, who had limited to none (Preservation definitely could see the future, though not really well).
From a human perspective, the difference is probably academic. Ruin wanted to end the world of Scadrial, after his brief fling with helping create it. Odium likewise seems to want to end Roshar, although whether this is just what he wants or whether there is more to it (it's implied Odium can't move on until he wins) we have yet to learn. Both Shards have the tendency to corrupt or take control of mortals to do their bidding. So from a human face, they are likely equally evil.