For us normal mortals with proper metal bikes grease is grease. I use lithium based grease from Earnest Doe's. If it is good enough to keep tractors and combines etc going in all kinds of conditions then it is alright for bike bearings, which are steel balls in steel cups anyway. Normal, as opposed to fancy priced so called specialised greases, have done my bikes for the last 50 odd years and will carry on doing so.
I am no Luddite, and know that there are some areas where specialised lubricants are advisable, but not on any bike I can afford!!