I have my Power Settings set to shutdown the monitor and stop the HDD after 15 minutes of no activity.
Is there any additional advantage to going into Standby when am not going to use the computer for a while?
Standby shuts down most of the rest of the computer as well. The CPU and memory will shift into a mode where they consume very little power, just enough to keep information in memory and restart operation without a reboot. It definitely cuts power consumption by a pretty significant amount. Your computer, idling with the hard drives and monitor shut down, might consume 50(ish) watts or so. In standby that same computer will consume somewhere closer to 10 or 20 watts.
(Of course, Your Wattage May Vary)
When I hooked up my EEE Netop it dropped to around 3 watts on standby according to my Kill-a-Watt. Since this is in night light territory it didn’t seem worthwhile to actually turn the computer off when I go to bed. My netbook actually pulls less than a watt on standby.