What's Your Definition of Best?
Do you mean the easiest? What about the actual dirt pickup? Does that matter?
When I vacuum carpeted stairs, I primarily have one one goal: dirt removal. So the machine of choice must have reasonably high agitation and as much airflow as possible. Think 150 nozzle CFM. That would automatically knock out canisters, central vacs as well as hand held vacs.
If you haven't guessed it already, I use a newer Kirby in portable mode. If/When I develop some physical restriction, I may use something else.
Bill