Even that's not necessarily so black and white, however.
For example, here's the top parse as DPS for BOTH WHM and SCH on Eden Prime (same run, they ran together):
https://www.fflogs.com/reports/fmWKC...pe=damage-done
While the SCH does have higher healing here, note that the SCH is still parsing 46th percentile healing, whereas the WHM is parsing 9%. One might argue that this is a tradeoff where SCH has an advantage...or one might argue how the WHM had 53% overheal (as compared to 35% for the WHM). Another argument might be that this is strategic, focusing entirely on oGCD healing and pure weaving on the part of the WHM (here roughly 75% of the SCH healing was oGCD or instant [hardcasts being 5 Succors], and roughly 82% of the WHM healing was as well [hardcasts being literally one Cure3 and two Medica2 casts]). (Note that these were all hardcasts, as all usage of Swiftcast by either player was added to their primary damage ability.) Like I said, to put it matter of factly is, IMO, pretty wrong unless you have some serious backup to support that.
This difference can also be seen on the DPS end, with the SCH only having 77 casts of Broil3, compared to 83 casts of Glare from the WHM, as well as some slightly reduced DoT usage (9 Biolysis vs. 13 Dia).
If one was to dig deeper, though, this is probably a good starting point, as overall activity was similar for both healers here (138 casts, or 24.9 CPM from the SCH, and 137 casts, or 24.8 CPM from the WHM).
For a bit deeper looking, here's another top-performing WHM on DPS...coupled with a high performing...WHM on DPS. https://www.fflogs.com/reports/z3xfD...pe=damage-done
One WHM parsed 99% DPS but only 9% healing....but the other parsed 77% DPS...and 86% healing. This suggests that it may not necessarily be a tradeoff as much as suggested.
Also supporting this, the highest ranking AST log (https://www.fflogs.com/reports/7zthZ...pe=damage-done) also features a SCH who parses well on both DPS (92%) and healing (77%).
Finally, here's another parse showing a WHM parsing both more DPS and healing than SCH...at a high level (97% DPS on WHM, 99% on SCH): https://www.fflogs.com/reports/QZbMq...9&type=healing