So according to a few online sources, there are certain weapons that can and cannot be specially upgraded. For this case, I'm considering the Iron Mace and the Mace.
The Iron Mace does not have Special Upgrades, and a Specially Upgraded Mace can overpower the Iron Mace in terms of Max Damage.
Mace: 94 Max Damage (monster drop/upgraded/Artisan/Special)
Iron Mace: 85 Max Damage (Smithed/monster drop/upgraded)
However, should I use R type or S type Special Upgrades?
If I use R type, the maximum damage will drop 13 (which is lower than Iron Mace). However, if I choose to do so, I'd upgrade the Mace focusing on both Critical and Max Damage (thus having a higher critical chance to do higher critical with R type upgrades).
S type is pretty self explanatory; having higher damage consistently than the Iron Mace.