One thing a lot of people tend to oversee is how the class works. Not the skills, but how the class functions as a whole. The main reason why a lot of people LOVE scholar--aside from their shields, mitigation and DPS boosts--is because of Lustrate.

Now why do I say Lustrate? Because there have been a variety of posts complaining about Lustrate vs. Benediction. But why is this the case? It's because Scholars can do more things between global cooldowns (GCD for short) than White Mages can. And because of this, it enables Scholars to throw in that beautiful clutch Lustrate onto someone while simultaneously throwing out 300 potency embraces on-top of Adlos and Physicks.

So when looking at a Scholar as a whole, they have essentially two global cooldowns and a variety of off-gcd which enable them to output more skills per second. When doing anything as a Scholar, you have three things to do per GCD rotation:

[1] GCD Skills.Aero, Cure, Stoneskin, Protect, Physick, Succor, Adloquium, Leeches, Ruin, Ruin II, Bio, Bio II, Miasma, Miasma II, Resurrection, Shadow Flare, Summon, and Summon II.

[2] Fairy Skills.Embrace, Silent Dusk, Fey Light, Fey Glow, Whispering Dawn, Fey Covenant, and Fey Illumination.

[3] Off-GCD Skills.Surecast, Swiftcast, Lustrate, Sacred Soil, Aetherflow, Virus, Cleric Stance, Eye for an Eye, Energy Drain and Bane.

Now looking at White Mage, the OP has already pointed out White Mage's strengths and weaknesses. Especially how Regen cannot be compared to an Embrace.

Quote Originally Posted by Slib View Post
Regen doesn't come close to what Eos heals for on a single target.
Agreed. Embrace has a 300 potency whereas Regen has a 150 potency over a 21 second duration (1050 total potency). Up-front healing is almost always better than heal overtimes as it puts you ahead in healing when it comes to HP per second vs. Damage per second.

Let's see... What else... Oh. A Tl;dr.
When a group is well experienced in a dungeon and is only taking unavoidable raid-damage, Scholars excel because the bulk healing White Mage's have isn't needed. Therefore, the enables Scholars to rely on their second GCD cooldown set (Fairy) to heal while they can DPS and do a variety of other things.

And and and and. Regen =/= Embrace. It's sort of like that question asking you if you'd take 1000 dollars now or get 1000 dollars every 5 years for a total of 50 years ($10000)