I have always used focal reducers/flatteners. 1st on a WO 80 Megrez to bring to focus. Also on a AT111ED and TMB130SS. Nither of those scopes had a manufactured dedicated reducer/flattener. The WO reducers I have owend worked OK, but didn't flatten the field well. That may have been caused by spacing issues. I ended up using the Astro Physics 27TVPH on the TMB which is not a flattener, but It worked well.
I now use the Takahashi QE-0.73x on my FSQ106ED and the Takahashi RH-QB 0.73x on my FSQ85ED. Even though both those scopes or flat field, the small 3.76 pixels signal will be increase by 100% according to John Hayes' Excel spread sheet calculator. Of course the field is increased, but the S/N also with shorter exposure times. According to John Hayes caulator I would need to double my exposure from 5min to 10min at F5/F5.3.
I also use a Astro Physics Quad reducer/flattener on my AP130GTX. Works exstreamly well. Without a flattener Iand with an APS-C chip there is curvature in the corners. A flatten would remove that, but with the current 3.76 pixel in the APS-C chips the S/N is greatly decreased. The flattener is a little less expensive, but bothe require correct back focus. So, I prefer the reducer over the flattener (which I have, but haven't used yet).
I realize that the three above scopes or expensive with limited avalibility. But to make a blanket statement that reducers do this or that, is often based of lower priced scopes/reducers with lower tolerances and QC. Those statements need to be referred to the brands experienced. Reducer/ Flatteners can have bad representation. That is usually with lower priced refractors and reducers. You can't cheaply reproduce either at consistant QC.
The advantage is wider field, shorter exposures which can improve S/N depending on exposure time. The disadvantage is getting back spacing correct. But a flattener will also require that. They can also be very expensive depending on brand. Even if you crop the image maintaining the pixel alignment grid, the S/N doesn't change. Not sure about resampling. It can also be more difficult to control camera tilt, which I am dealing with now on the FSQ106ED with 3.76 pixels. That's just going to need a few nights with a small hex wrench.
I must also metion my backyardh has a very limited field of view. Clear nights are few and Bortle 7. SO, I do narrow band and time is limited.
Lynn K.