I recently measured disappointing bath fan flows at a project - both being below our program minimum of 50cfm. The builder had the installer come back to have a look and found nothing obvious but he did get a couple of new fan motors and swapped them out and also double checked that the damper flap wasn't stuck. There was a slight improvement to both but it was not enough, still both below 50.
These fans were routed - with a short run of duct - to soffit terminations which allowed us to look up inside and check for blockages but none were seen.
Then the weirdness: I checked the flow coming from the terminations and both were about 90cfm, yet still only about 45 inside. How can this be? I've never seen this before, but that's because I never test at the outside.
I hate to bash brands but these were Broan fans which I rarely see used around here. Most all of my contractors use Panasonics.
In my opinion venting into any soffit is a bad idea, it usually requires a sharp bend to get into the soffit, and reduces insulation value where it crosses the top plate. (significantly) Better going through the sidewall or box/gable, nice straight run with an extra damper thrown in that doesn't put back pressure on vent pipe. Additionally the hood damper seals much tighter (typically) then the inline damper that is provided with fan.
In my northeast climate (zone 5 & 6) adding damp air to roof edge in 0deg weather is asking for icing issues.
Never had issues getting fans up to needed CFM when running through wall. Usually issue is related to air envelope tightness where the fan struggles due to lack of fresh air intake. This can be detected by opening the bathroom window (or any window) while testing to see if it affects flow rate. (I've seen that it does)