The 38mm fans push more air, usually have beefier motors, and show a higher air-pressure at the exhaust side.
All of these things make them a better choice, barring the fact that they never come with integrated LED lights.
The beefier motor often is capable of higher rpms, and gets rated for noise in the unacceptable range above 50 dBA. Consider, though, that often -- with a better quality motor -- this noise may be due exclusively to "top-end air-turbulence." But you aren't going to need to run it at the "top-end." And with an occasional exception (like the Vantec "Tornado"), these types of fans are as quiet as a Scythe or Yate-Loon running at comparable speeds. The difference arises when you can program a fan-controller or motherboard to rev the beefy fan up a tad as temperatures rise.
Unless you have some issue or limit pertaining to the overall weight of a CPU-cooler-plus-fan assembly, the better 120x38mm fans also weigh a bit more. Some of the better Panaflos weigh in at an excess over 250 grams. Same with some models of Delta, although I've found a Delta that's quiet at 2,500 rpm and weighs about 50 grams less than a Panaflo capable of the same CFMs.