As often pointed out (by mena among others) you still need the inverter for the DVD even if the TV is 12v so might as well just plug them both in the inverter.
You can get a theoretical advantage by having a big and small inverter, but as agreed in this thread by several posters, it is trivial if you can detect it at all.
EG, I found some time ago that I can use a CFL bulb instead of a regular 120v bulb in the reading lamp by our RV couch. (we have some 120v lights as well as a bunch of 12v lights) (Didn't go the LED route except for one night light sort of lamp)
On inverter (any size) the CFL bulb has the inverter pull 1 amp from the battery instead of the 3 amps the 12v light pulls, and the CFL even provides more light for reading.
My point is that I still get the same 1 amp draw using the 3000w inverter to run it, as I did with the small inverter I had on that job before. So no advantage seen there at all with that very tiny load.
