You trust me? Oh, my...
A hard reset doesn't change the software, it just removes all third-party apps and user data, then gives you the option to restore from your backups when you sign back in to your Microsoft account. So, if you have 8.1 Update 1 before, you will still have 8.1 Update 1 after. If your backup is good and you choose to restore, all of your apps will reinstall, your settings will be recovered, and your start screen customizations will likely come back. Any files on your phone - pictures, music, documents, etc. - will be deleted, so you need to make sure you have them backed up to the cloud (OneDrive or what have you) or a PC so you can get them back. Any user data in apps that don't back it up will also be lost, which means things like game scores and ranks will vanish. Unfortunately, most of those can't be recovered.
The Nokia Software Recovery Tool is an application that you download and install on a PC. It wipes your phone just like a hard reset, but it also replaces the firmware and software on your phone with the 'current production version' for your specific model and variant, per Microsoft Mobile's records. This may be Black firmware and WP 8.0, or it may have recently been updated to Cyan firmware and WP 8.1 (saves a lot of work if it's this one). When it's done, you may still have to run update to bring the phone to the most current version released for your variant, and then you'll have to install and enable the Preview for Developers app if you want to bring it up to DP Update 1 again. You can then hard reset and restore to get back as much of what you have now as you can, same deal as with the hard reset above.
Before you do either of these, make sure your backups are good. Go into Settings, backup, and manually run the apps+settings backup, then check to be sure you have backup turned on for text messages. Lastly, make sure you have all your files copied off to the cloud or a PC.
Please ask if you have any more questions or if any of this isn't clear. Good luck!