Thanos wins easily. He's an eternal, he has matter/energy manipulation powers, he's a telepath, a telekinetic, he's WAY faster than Doomsday in landspeed, agility, and reflexes, he can project psionic force blasts, he can project cosmic energy of any intensity, he's stronger than Doomsday, It is nearly impossible to injure him by any means.
These are Thanos's abilities without any enhancements such as the IG.
Doomsday is so outclassed it isn't even funny. He'd never be able to hurt Thanos. Thanos would obliterate him in seconds.