I use both/either depending. The strop as a finishing step generally less QC for burr formation, much more forgiving of angle control in some respects as long as you don't go too broad with it, not very tolerant of pressure variation unless using the harder forms.
Finishing stones require better angle control and are equally if not more intolerant of pressure variation. In general the stone finished edge will be more precise but more challenging to create, stropping is the reverse. As Andy mentions, for most it comes down to slight changes in final edge character. Depending on how its approached the actual difference might be very slight.
Stropping can be as inexpensive as a sheet of paper wrapped around a benchstone or dry waterstone and seeded with waterstone grit or honing compound. Try both. For many, the strop becomes a crutch, but used properly is a nice finishing option. Using a fine finish waterstone will challenge your skills, which can only help all other aspects of your work.