My Coleman Mach air conditioner came with a hard-start capacitor already installed.
I replaced it with a soft-starter with good results. I can run my air conditioner using a modest generator, but I rarely do. It also reduced the clunking sound when the compressor first starts, which is nice.
The two technologies are totally different. The hard-start capacitor stores electrical energy which it then releases into the compressor start winding on start-up. The soft-starters, such as Easy Start, work by limiting the current to the main (run) winding during start-up and allowing the current to ramp-up over a quarter of a second or so. The result is far less in-rush current and a smooth start.
As stated, there is much more posted here if you do a search for it.