I'm with dabac here, that most differences you feel when converting a given bike from derailer to singlespeed (not fixed) are placebo.
But it's important to note that ANY EFFICIENCY GAINED BY GOING SINGLESPEED IS MORE THAN LOST BY FORCING YOUR BODY TO PEDAL AT INEFFICIENT RPMs when on terrain or wind conditions that aren't perfectly optimized for the gear that you chose.

(Things are a bit different with fixed-gear because the chain will actually push the cranks forward through dead spots in the pedal stroke, so it definitely feels different unless you have a super-efficient pedal stroke.)

That said, riding a singlespeed is fun, and requires minimal maintenance. My bad-weather road bike is a singlespeed (with fenders) that I ride with impunity in downpours. I highly recommend it. Just not for efficiency's sake.

As for gearing a singlespeed, it's a compromise between a small enough gear to make it up hills and a comfortable cruising-speed gear with a tailwind or slight downhill. You can test this out well enough on your geared bike.
If you go fixed, since you can't coast you have the added concern of a gear big enough that it won't force you to spin out on a big downhill, which is one of the scarier feelings I've had on a bike.