I have used Sudowoodo in my Crystal playthrough and I didn't have a problem with it.
A lot of Geodude's value comes in having favorable matchups against all of the first three gym leaders, where you won't be able to get Sudowoodo early enough to contribute in those battles at all. Having Ground as an extra type also means you can dominate the Magnemites that appear on Jasmine's team as well as the rival's.
Ok, so let's see these Pokemon. (I will be using the original gsc, if you want hgss I can do that)
Sudowoodo: Excellent Defense Excellent Offense Decent HP Decent Special Defense Alright Stab in Rock Slide Amazing Ground Coverage with Earthquake Horrible Speed Not much else coverage that is physical
Golem:
Excellent Defense Excellent Offense Decent Special Defense Decent HP Very good Stab with Earthquake. Not the best movepool Rock throw isn't very good stab Not much coverage again
I still would say that golem is better. However, if you can't trade choose sudowoodo ANY day