A couple of things to consider with a fixed gear vs multi:
A fixed gear will force you to pedal whether you want to or not. When the road goes downhill, you'll pedal your butt off trying to keep up with the cranks, since the pedals move when the wheels move. This can really smooth out your pedal stroke and point out a lack of leg muscle coordination. With a multi-gear bike, you'll freewheel when the pedal stroke kicks up.
When facing any kind of head wind or hill, you'll continue to develop a smooth stroke/cadence as you attempt to maximize output and efficiency. When the extra gears are there, the temptation to use them is often too great.
There is a different "feel" when pedalling a fixed gear bike. You feel more "connected" to the pedals, cranks, chain and tires.
Pedal forward, go forward; pedal backward, go backward. Kind of Yin and Yang, or "wax on, wax off."
Which brings me to the best thing about a fixed-gear - try riding one without brakes (like a "track" bike)...HOOOWHEEEE...you'll soon learn how fast a bike can go from 30mph to zero with "back-pressure" applied to the cranks.
Plus, you can do cool "trackstands" (balancing upright by applying forward and backward pressure - like track riders do in the sprint competition) at the traffic lights!
Can you get a great workout by riding in a single gear no matter what the condition? Sure, but there is a different feeling you get riding a fixed gear. I don't know if you compete, or ride with other riders who do, but if you can find someone who has a track bike, ask to take it for a ride and feel the difference.