It's not a question of how much PSI it contains. It's the speed it can enter the tire assembly. Small volume compressors don't move enough CFM at times.
The C02 cartridge can help if the tire bead seal has been broken as it produces a faster fill rate than a 12V compressor. If you ride in a group probably wise to have both.
You need to be correctly sprung for your weight. If you have original springs they're trash. Spring it as a base line.
My stock suspension up front was undersprung and underdamped. It dove HARD on braking.