A strong breaking point for my decision would be whether or not the two games have loads of flavor text. Imagery only goes so far: I love to read aloud details that encompass more the tone of the game (as Mansions of Madness does so well). I also enjoy games that have flavor text for victory and defeat I found too.
Flavor text is more to be found in Runebound, clearly distinguished by italics. The same goes for Arkham, even though the italics are seldomly used. The cards are written in a story-telling manner and almost all text can be considered for flavor. Arkham Horror has flavor text (and game impact) for success and failure in most encounter cards, but don't expect too much.
Though I have heard Arkham is the better rated, Runebound has a competitive play mode too. Cooperative play is a must however. I know Arkham has cooperative play covered but I wondered if Runebound can do that too. Replay value is also important to me: how far do the expansions take the games?
The popularity of Arkham Horror will always be a mystery to me. I simply can't understand how such big audiences are attracted by a boardgame with Lovecraftian setting, hundreds of cards and a fake RPG-look. It might be a better game than Runebound because of its incredible variety, but it has limits and subtle balances that Runebound has not. Runebound is solid, perhaps monolithic; Arkham Horror is variable, not always fair to the players, not always a challenge. Very random, but ultimately entertaining.
If cooperative play is a must, you can forget Runebound. This game has no real co-op; JCHendee has hinted at the experiments made in the different expansions, but ultimately there's not a real co-op play except homebrew stuff. The only "real" co-op expansion is Midnight, where one player (Shadow Lord) is set against the others (Heroes), who can and possibly must cooperate to win, Midnight is out of print and wasn't well received by the public. Too different. I've never tried it yet, never had the guts to propose it. Arkham Horror is only co-op and there's no real competition between players. They have to help each other and coordinate their efforts to save the world from the awakening of the Ancient One.
Solo play can be done in both games but Arkham has too long a setup IMO. I played it 3 or 4 times alone, but it took too much to prepare everything. Runebound doesn't require that preparation and is very interesting if played with some variants that give you a limited time, otherwise your victory is just a matter of time and it's pretty pointless in terms of learning and challenge. There are better pastimes.
Replay value is very high in both games, considering all expansions. Runebound has many card expansions which give you the variety that you won't find in the base game after 10+ games. The big box expansions bring the changes to a deeper level and are recommended because they add new Heroes and a new setting as well. Arkham base set has so many cards that you won't need new material for variety's sake; you'll need it to increase the challenge, as the base game tends to be quite easy for experienced players. All expansions add a lot of stuff, perhaps too much, and it's very difficult to decide what to use and what to save for the next time. I noticed that most expansions change the game but their potential is not to be seen, as there are few chances to visit different places, draw new cards or achieve extra stuff. If your investigators lose time hanging around, they'll probably lose the game. So, new stuff plays a minor role, components tend to get diluted and I don't know how to put this bunch of material into real use.
I hope that my confuse flow of thoughts can help you.