Is it okay to uninstall the old versions of iWork/iLife after their respective upgrades that come with OSX Mavericks?
You can uninstall them if you like. Apple leaves them behind so you can compare the feature sets and UI redesign to see if you want to use the new apps or retain the old ones. I personally dislike the new design, as it is too simplified and was missing some key features, at least in Keynote, which I use the most.

Remember, though, that whenever you click on an iLife document, it will always open in the new app. If you set the default app on a document to the old iWork app in a Get-Info window, Finder will soon change it back! Even worse, Software Update will pop up a daily asking to upgrade to the the iWork apps, with no way to turn this notice off.

Insidious nonsense.