I saw a post in another thread comparing the DPS differences between WHM and AST a while ago and that inspired me to do the same thing, but with all three healers. All the data was pulled from fflogs a few days ago during week 7 so it should still be fairly representative.
Here are the DPS thresholds for various percentiles for each of the encounters. I bolded the top DPS in each category.
---Chaos---
99th: AST: 4218 SCH: 4182 WHM: 3620
95th: AST: 3734 SCH: 3689 WHM: 3241
75th: AST: 2991 SCH: 3034 WHM: 2685
50th: AST: 2565 SCH: 2449 WHM: 2267
25th: AST: 1923 SCH: 2089 WHM: 1844
---Midgardsormr---
99th: AST: 3524 SCH: 3530 WHM: 3206
95th: AST: 3141 SCH: 3132 WHM: 2864
75th: AST: 2566 SCH: 2585 WHM: 2419
50th: AST: 2160 SCH: 2234 WHM: 2107
25th: AST: 1803 SCH: 1908 WHM: 1802
---Omega---
99th: AST: 3871 SCH: 3827 WHM: 3245
95th: AST: 3403 SCH: 3355 WHM: 2944
75th: AST: 2791 SCH: 2766 WHM: 2486
50th: AST: 2393 SCH: 2413 WHM: 2199
25th: AST: 2024 SCH: 2097 WHM: 1905
---Omega M/F---
99th: AST: 3586 SCH: 3589 WHM: 3380
95th: AST: 3164 SCH: 3208 WHM: 3028
75th: AST: 2617 SCH: 2718 WHM: 2559
50th: AST: 2245 SCH: 2398 WHM: 2247
25th: AST: 1924 SCH: 2107 WHM: 1958
---Final Omega---
99th: AST: 3776 SCH: 3815 WHM: 3577
95th: AST: 3363 SCH: 3387 WHM: 3113
75th: AST: 2732 SCH: 2772 WHM: 2534
50th: AST: 2225 SCH: 2425 WHM: 2241
25th: AST: 1963 SCH: 2116 WHM: 1984
---
AST and SCH appear to be pretty neck and neck in terms of DPS in a lot of these fights, with only a single digit of difference between them in some cases. In none of these fights in any of the selected percentile categories does WHM come out on top.
Unless you are solo-healing or doing something uncommon like doubling up on healing jobs, you will be paired with another healer of a different job. Because of this, its also interesting to look at the pick rates of all the healer compositions. I made a quick bar graph displaying the composition pick rates based on the number of unique pairs of healers who are ranked for each fight.
Number of unique pairs of healers with clears for each of the fights:
---Chaos---
SCH/AST: 7821 SCH/WHM: 10232 WHM/AST: 6081
---Midgardsormr---
SCH/AST: 5990 SCH/WHM: 10395 WHM/AST: 3421
---Omega---
SCH/AST: 4693 SCH/WHM: 6539 WHM/AST: 1639
---Omega M/F---
SCH/AST: 5799 SCH/WHM: 4440 WHM/AST: 461
---Final Omega---
SCH/AST: 2234 SCH/WHM: 1302 WHM/AST: 105
Pick rates in graphical form:
SCH/WHM Starts out popular in the lower floors and is gradually overtaken by SCH/AST by the later floors. For AST/WHM however, the pick rate gradually gets worse in later floors, bottoming out at a measly 2.9% pick rate among cleared healer pairs for Final Omega.
There are probably a lot of reasons why the pick rates are the way they are, and I don't feel I am really qualified to discuss them at length. I hope this data can be useful to somebody though.