Using the upgrade utility is not "another option"; you must use it to upgrade your system. You can update the RTE and web tier to 9.33 but if you then just connect to the production database, you will stil be running 9.21 applications (the applications are part of your database data and the only way to update them is by using the Application Upgrade and Application Patch utilities).
You need to: --update the server software/ RTE --update the clients --use the upgrade and patch utilities to bring your SM applications up to the new version. --generate a patch which can then be used to update production.
--TEST the patch repeatedly against a production copy until it is validated. This is the single most important part of the process. Repeat testing until you are intimately familiar with the process to apply the patch and have verified the resulting system is correctly upgraded. --use that to upgrade prod.
The attached HP document outlines the specific steps for an upgrade from 9.20 to 9.33 (Because 9.21 is a minor release, this is the appropriate guide--there is not a separate guide for 9.21).
Problems we've encountered with customers (don't do these :-)
Skipping the entire application upgrade piece (e.g. upgrading only the server RTE and clients).
Applying the application upgrade, but not completing the reconciliation process to resolve conflicts between tailored objects and any objects modified in the new application version. This can have, um, hilarious results.
Not testing the patch against a production copy until right before they've scheduled the upgrade of production, leaving no opportunity to correct any issues.