I have done comparisons between 737-800(W) and A320s (CFM56-5B and IAE V2500-A5) in the past using the numbers from the manuals used.
There's never a clear cut on which is more efficient etc, that's why there are several comparions above.
Note there's a 20ton payload fuel burn comparison, instead of all the comparisons being based on seats, as seat configurations can change, depending on what the airline configs are, etc etc etc.
If fuel is cheap, the 738W is probably the way to go (and it's faster on Long Range Cruise). If fuel is expensive, you'd definitely consider the 320 if your average sector length suits it. And if you go for the 320, if fuel is cheap, go with the CFM56s, their maintenance is cheap, but if fuel is expensive, the savings on the maintenance easily gets eroded by fuel costs (but also remember those IAE engines are not cheap either).
More power? Depends on your engine options.