Okay, Engels has a + so it has the AP advantage here by quite a lot. Base Luffy scales around 170KT and much higher with Gear Second and even higher with Third (almost able to one-shot Zoan Lucci) so he can close the gap a bit with it.
With that being said, I think Luffy should take this. I don't know Engels' size since the page doesn't say how big it is, but it has a weakness of lacking agility and smaller opponents can climb onto it, which is something Luffy would do. He's not only hilariously more agile thanks to his physiology but able to get fast enough to blitz it with Gear Second, so the difference in power would matter little in this case since Engels wouldn't be dealing any damage.
Electricity Manipulation is useless against Luffy, and any rangd options gets lolnoped by Gear Second's speed amp.
Granted, Luffy'd have a hell of a fight trying to destroy Engels considering its durability, but he has a big room of opportunity to destroy it considering he has the speed advantage by quite a lot.
Since, this is apparently Enies Lobby (though why not Thriller Bark) Luffy, in his Base he is scaling to Base Lucci who is above 172 KT and his Gear Second is scaling to 285 KT. And of course, Gear Third scales above that by a lot.
Engel apparently has a feat that put him at 719 KT. So he is 2.5x stronger than Gear Second Luffy.
Some disadvantage for Luffy would be that of Engel's Self Destruction and that the robot has a higher lifting strength.
That being said, for now, I will place my vote on Luffy for Calaca reason above. He does addresses a lot of good points on how Luffy can handle Engel despite the AP disadvantage.