I have run into three one-armed bandits in playthrough 1 (and zero in playthrough 2 sadly). The first was in Fleshstick's camp, the second was in The Fridge (just before the cliff above the cristalisks), and the third was in Sawtooth Cauldren while doing the side mission for raising the flags (he was in the last flag camp). I have found the cost of the slot machines the one-armed bandits carry to be the same as all the others and the odds of a useful payout or a legendary to be exactly the same as well.
The cost of a spin on any slot machine appears to scale to storyline progress and playthrough. So a lv 50 that was power-leveled from 1 to 50 in another players campaign but never completed their own campaign in playthrough 1 will be able to play the slots in sanctury when they first arrive for next to nothing whereas a lv 20 that would likely have only just reached The Fridge or perhaps sanctuary after it starts flying, would be paying upwards of 400 or 500 a spin (possibly more it's been a while since i was lv 20). By the end of playthrough 2 it's in the thousands of dollars a spin and very rarely are you going to find something better than what you have gotten from killing bosses.
Also, the level of the guns you get from payouts is scaled to your storyline progress so if you take that power-leveled character and sit at the machine in sanctuary (in your barely started storyline) and are lucky enough to get the 3 vault-hunters/borderlands symbols; the legendary gun you get will be about level 7. Not exactly useful to a level 50 character.
As for odds of a payout (especially a useful one); there are many videos on youtube that suggest one or another having better or worse odds, but as someone who has played all of them for upwards of 10 hours each; the odds on any machine are about the same. Sometimes you will be lucky and get 2 eridium jackpots in a row, sometimes you will get a granade 10 spins in a row. Overall you are most likely just going to get tons of useless vendor fodder guns (Vendor Fodder: an item only useful for selling at an ammo/med/gun machine), a mess of different player skins, and some of your cash back.