Many of the up-scale O/U comp shooters will use only the specialty product S.T.O.S. (Slicker Than Owl S**t) from the Ponsness/Warren reloader folks. I've used it and RIG (standard and type P) and Mobil 1. I went to the synthetic more to protect the engraved in-the-white receiver of one of my guns than for it's lubricating properties.
Years ago, I asked Lucio, the Perazzi factory wizard, just what was the lubricant he was brushing on my guns' friction points. His answer: A 50/50 mixture of Vaseline and 30W non-detergent motor oil. It's not so much what grease you use but how you use it. Most comp shooters keep their O/Us in a hard case, so it's broken down and wiped down every time they shoot. So, the grease doesn't have to be long lasting. There's a gun club ritual: long after the stick guns have been stuffed into their cloth sacks, and their owners hit the highway, the comp shooters are still beavering away at their O/Us.