uhhhh 757man... no 737 or A320 is powered by CF6s
(which powers some 747s/DC-10s/767s/A300s/
the 737-600/700/800/900 is powered by CFMI CFM56-7 turbofans and the A319/320/321 has a choice of CFMI CFM56-5s or IAe V2500 engines. The A318 will also have CFM56s but also the new PW6000 engine.
Now then, comparison: (note when i reffer to 737 i reffer to the 737NG, not necesarilly all 737s)
The A320 has a wider cabin than the 737 and a higher cruise speed. The 737 is slightly cheaper. The 737 can be ETOPS certified. The A320 is full fly-by-wire, the 737 is not. The A320 has outsold the 737 outside the US and about broken even inside the US (A320 got UA, US, AW, NW. 737NG got AA, CO, DL, SW, AS).
As mentioned above the A320 comes with an engine option, the IAe gaining orders because it has better FOD rates and lower fuel burn, though the CFM56 is cheaper to maintain.
The A320 sits higher up than the 737. The 737 uses less runway in most conditions for a similar stage length.
Safety records are better for the 737, but are statistically irrelevant at this point because the A320 is 6 times the age of the 737NG (compared to all 737s, the A320 comes out about the same in terms of accident rate).
Well i think thats about all the authoritative true facts i can give without getting into personal opinion...
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