pond heater vs. de-icer

We just spent all summer building a 10,000 gallon pond which is 5'
deep (3' underground, 2' above). We can't decide between a $30
floating de-icer and a $1,000 propane heater. If the cost to run the
propane heater is cheaper than the electricity cost for the floater,
we'll go for the propane heater. Does anyone know the relative costs
of these two types of heaters? Also, which is better for the koi?
Finally, if anyone has used a propane heater to keep the entire pond
ice-free for the winter, which one do you recommend.
Any input is much appreciated.
Dennis