You can set what type of notification connection requests sends within CB > Configuration > Connections and adjust "Notification Method" as necessary. You can do Email, PMS (with UddeIM), or both. PMS is probably most similar to Facebooks usage.

The only other module that shows pending connection requests is the CB Workflows (mod_comprofilerModerator.zip) module included with the CB package. You could also set Notification to PMS, have UddeIM installed then use the UddeIM module and it'll let them know when a new message is available. They'd check that message and it'd be for a new connection request.