Another inverter question!

MP soldier wrote:
If you have a 1,000w inverter running an LCD tv, and a 2000w inverter running an identical LCD tv. Does the 2000w inverter use more battery power?

You see, I bought a 2000w inverter to run my microwave, and it doesn't....Don't ask. There is a 7 page thread on here about that mess.

So now I have a 2000w PSW inverter powering my LCD tv. Overkill much???

I'm just wondering if I should try and barter for a smaller inverter because the 2K watt may be wasting more of my battery than a 1,000 watt would.