I had to restore my iPhone from a week old backup in order to get the previous Uber version back. It's a shame there's no easier way to downgrade an app on iOS.
There is, but only if you update apps in iTunes on your computer instead of directly on your iPhone.
Basically, update the app in iTunes (which will send the old IPA package (which is still signed to your Apple ID) into the Trash / Recycle Bin, then connect your iPhone to your computer and sync to replace the old app with the new one. You’ll still have the old IPA package in your computer’s Trash / Recycle Bin, so if you ever need to downgrade to the older version of the app, just move it out of the Trash / Recycle Bin, delete the newer version of the app in iTunes, and then double-click on the old IPA package to have it open in iTunes. Then, you can just connect your iPhone to your computer and sync.
Basically, update the app in iTunes (which will send the old IPA package (which is still signed to your Apple ID) into the Trash / Recycle Bin, then connect your iPhone to your computer and sync to replace the old app with the new one. You’ll still have the old IPA package in your computer’s Trash / Recycle Bin, so if you ever need to downgrade to the older version of the app, just move it out of the Trash / Recycle Bin, delete the newer version of the app in iTunes, and then double-click on the old IPA package to have it open in iTunes. Then, you can just connect your iPhone to your computer and sync.