The old white lithium grease is different than most of the modern lithium greases. It's thinner with fewer additives. As a former farmer I would not use white lithium grease to grease $$$ machinery, modern EP lithium complex greases are much better for that. And in a lot of cases they are almost black when new.
Example, old bike hubs didn't have seals, you could peer through the gaps and see the bearings in the races. If the grease that was nice and white when fresh looked pretty dirty inside the hub, it was time for an overhaul. Pro team mechanics would be doing teardowns and overhauls on a regular basis. And thinner grease gave faster times.
When I do an overhaul on my bike with sealed hubs and all that, I want to go as long as possible before having to do it again. So something like name brand marine grease would be the best choice for me.