I've been reading through earlier changelogs, there used to be a difference in cost between 'minor overhaul' and 'major overhaul', but I'm pretty sure at the moment sending a ship to overhaul doesn't cost any additional maintenance over the normal maintenance cost.
Though you save resources by having a ship out then sending it into overhaul, (since overhaul reduces the clock by a factor of 3 or something) it's offset by the maintenance supplies cost whenever a component breaks.
Of course maintenance supplies only cost duranium, uridium and gallicite so it could be possible to strategically use MSP instead of overhaul and maintenance in order to save other resources. Or if a ship is being scrapped soon anyway.