RIght, but I do feel like the fights often are designed specifically with a whm/sch pairing in mind. plenty of raid-wide damage and tank killing moves but with enough time in-between that with proper lustrate management means sch usually can have those big heals handy. It's all about knowing the fight/ the pace. And not being afraid to blow a Lustrate when it's time but knowing when it ISN'T time as well. SCH really do excel at tank healing by keeping them up and shielded and lustrating when they get too far down.

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A bad sch is made by:
improper fairy management
improper aetherflow management
little or inconsistent use of adlo
spamming adlo til oom instead of weaving in physics and lustrates
improper use of other cd's

A bad whm is made by:
cure2/cure3 spammers - not using enough cure1 for freecure procs
inconsistent or nonexistent regens
poor timing for heals (many times you need to precast in prep for incoming damage)
poor use of cd's
overall terrible mp management

SCHs main tank healing is from adlo/physic weaving + properly managed fairy
WHM main tank healing is from regen + cure1 + freecure procs

SCHs main raid healing comes from preventative succor/ top-off succor with a possible sacred soil if not needed for a lustrate, but timing is even more important for that move. With Eos, they can use her aoe regen as well, but most SCH will be using Selene
WHM main raid healing comes from medica 1/ medica 2 depending on the situation. Under some conditions, a cure3 is great as well but shouldn't be the go-to raid heal due to its cost and radius. (a med1/2 is much better in many cases if people are spread out a little more and are more likely to also hit the tank where cure3 might not)

SCH have lustrate for healing up from low hp and its great for immediate relief after heavy hitting moves, plus adlo is great for preventing some damage from heavy hits anyways, and it's part of their main healing "rotation"
WHM have their potency cd/ spell speed cd and/or regen+cure2 for low hp tanks, and benediction which can usually only be used 1-2 times in a fight. For certain moves, stoneskin is important before a hit

SCHs manage hate automatically since they split potency with their fairy. Additionally, the shield portion of adlo I believe doesn't generate hate or very little.
WHMs manage hate through paced healing and SoS.

SCHs manage MP through weaving in physics and adlos properly, using lustrate properly, managing their fairy, and managing aetherflow, and of course timing/pacing
WHM manage MP more through timing/pacing, sticking with regen+cure1 as much as possible except for using that freecure proc. Good management of SoS is also extremely important. But it is more beneficial for the whm to spec PIE than the sch.

SCH dps is great for boss-type encounters. They can put up DoTs in clerics, and lustrate isnt affected by stance changes, neither is the fairy. fairy + whm + emergency lustrates are enough for many phases of boss mechanics for a good while. Additionally, bane works well for smaller pulls in dungeons. Still, have to be careful on timing with cleric's stance.
WHM dps is more lackluster for single-target; however, they excel at aoe damage. Holy does not have a target limit like bane does as well, so it works really well on very large pulls while also providing a bit of cc. However, Regen needs to be put up possibly with divine seal before-hand because benediction and stoneskin are the only moves really that arent affected by the stance change. So you have to be extra careful on the timing.

Both healers need to be using virus and eye for an eye appropriately and without accidentally both using it at the same time, so takes some coordination there. These skills are great in many situations and should not be neglected! But be careful because SCH virus has a little more utility, so in some spots they should definitely get priority on that move.

Raising - the general order for who does raises is SMN->SCH->WHM but it doesnt have to be that way. If a WHM is doing well on MP they can raise just as easily. My group often does it with that priority but also based on who has swiftcast up. Interestingly, if none have swiftcast up, the whm could try to use the spellspeed buff and then cast it for a faster raise.

Remember, for SCH, fairy management is about placement and targeting. and although in some cases you can use them somewhat interchangeably, aetherflow for mp is NOT the same as SoS for mp. So if you swap classes, you need to think of them a little differently:

Aetherflow is for mp management as well as Lustrate charge management (also sacred soil and energy drain, but Lustrates are more useful in a lot of situations since its instant off-GCD mega healing). Aetherflow is available very quickly (1 min recast timer?) and the mp gained is instant.
SoS is for mp management as well as hate management. Try to save it for the mp if you can!! But it can be good to blow simply for emergency hate issues. I try to save it til I need it for mp, and sometimes I will be in the yellow or orange before I get to that, but it only matters in the end if you take hate and get hit. Just watch for that. Also, it has a longer cooldown (2 min. maybe? I can't remember off the top of my head) and it is an mp regen not instant mp.

Keep in mind that while physic+embrace is about as powerful as a cure2 at the price of a cure1, the fairy can't embrace at the same rate as the sch's physics (it is slower). WHMs also have regen which people tend to forget to include in that. Regen should be up on a tank most all the time. And don't forget you can divine seal + regen for a really nice hp regen.

And most importantly for both classes -- trust the other healer! If you can't trust the other healer, you need to find a new one. or improve yourself (as maybe the actual case is the other healer can't trust you!). Healers work best if they are really in-sync with the fight's pacing etc. and also with each other. Knowing what the other healer is going to do helps you know what you need to do, so it may take a little time getting used to each other while also getting used to the fights. But it can really work well!