Stat difference isn't significant, but the effects are.
For slayer RoD might be better as you're quickly killing a lot of monsters leading to rapid adrenaline gain from its passive, though personally I don't like the additional cost from using it over surgeon there.
Hmm.. Okay, and what about the chance to get extra adrenaline from killing things? If there's a low cap I guess it'd have limited use?
Assuming you fight a mob with 7500 LP or above, you will gain an average of 2.5% adrenaline per mob killed (50% chance of gaining x/1500% adrenaline, x being the target's LP to a cap of 7500). In contrast, surgeon’s saves 15% adrenaline 10% of the time, averaging to 1.5% adrenaline saved per threshold use.
Assuming costs aren't an issue, it's best to use surgeon’s against tough mobs and ring of death again mobs around 8k LP.