From the two screens you show "Controller Summary" and "Inventory"; you are not going to see a whole lot different other than the newer features that are supported in 5.x and 6.x; however in 6.x there is now a Dashboard page which will displays alot of useful client and AP information. I wouldn't purely recommend you upgrade your customer to see more information on those two particular screens, but rather consider the newer features and enhancements in 5.x and especially 6.x that would make the upgrade worthwhile. The changes to 6.x are typically an easy sell for an upgrade from 3.4.x......although make sure you read the release notes about an "upgrade hop" when going to 6.x from versions earlier than than 3.4.4.1 (which from your screenshot you are).....or 5.0.3.1 on the 5.x train.