It can depend on the DVR, however,
is correct that there is not a lot of difference. Some DVRs have the iHDD spin down (after a while) when they are "off" (in standby and not recording). In that case you might save say 5W, however, 5W is almost nothing for short periods of time like leaving the room and the iHDD rarely spins down right away. With most of the older equipment, the difference was only 1W. See the following thread on the subject of parasitic draws. You may wish to purchase or borrow a Watt meter.
There are probably lots of other places in the home where you could save a lot more.
Although it's not the case for electronics like a DVR because they stay in standby, it's not really a good idea to turn most electronics on/off for short periods of time. (Most) electronics prefer to stay in one state or another and not constantly switching on/off. The contraction and expansion of the boards due to heat cause this damage. It's not as much of an issue with the latest electronics because they typically use less power and don't get as hot due to their design.
Although it's laudable to try to save energy, it's important to understand whether it's worthwhile and/or advantageous.
Standby just disables the HDMI port, it doesn't actually turn "off", so you won't be gaining much (if anything) by powering down more often. The spec sheets I have (albeit from years ago) indicate that the HDPVR 630 consumes roughly 139 kWh/year.
The major difference between the on and off states with BDU PVRs is that it buffers the current channel to disk when on and stops buffering when off. That might account for the 1W of power saving cited above. Most of them don't allow the disk to go into standby but keep it spinning at all times. The 2.5" disk in the 630 does not consume much power even when active. The main advantage to turning the 630 off is that eliminating disk buffering will extend disk life to some extent.
Standby just disables the HDMI port
It's not even clear it does that. Most BDU PVRs in this class simply blank the screen, similar to a PC screen saver. Turning the HDMI port off or putting it into a power saving state will result in a no signal message on many TVs. Blanking the screen will not.