I'm both a WHM and a SCH, so after a quick comparison here's what I found:
Unbuffed Pet: ~200 per tick
Unbuffed WHM: ~230 per tick
Buffed Pet (Rouse-Only): ~280
Buffed WHM (Seal Only): ~300
The above has the WHM with about 11 less MND, but 30 more det. However, even dropping to garuda's book on SCH (drastic drop in mind, weapon damage and det, leaving them obviously behind WHM) the pet it still doing 180 unbuffed. This means that, both buffed and unbuffed, the WHM currently beats out Eos on per-tick healing, though not dramatically. The diff is a bit bigger in a 4-man since SCH gets no MND buff from team without a WHM present, but that diff wouldn't me more than a few points. Biggest diff is about 30% right now given remotely comparable gear, which is a bit smaller than you would expect if the main-and-mend trait was ignored (they total 40%). Likely, the trait is taken into account but the pet is given some flat debuff in the 25% range.
The above means that post-patch will look as follows:
Unbuffed Pet: ~200 per tick
Unbuffed WHM: ~115 per tick
Buffed Pet (Rouse Only): ~280
Buffed WHM (Seal Only): ~150
Clearly the per-tick benefit goes notably in Eos' favor post-patch, though the total number of ticks is clearly in the WHM's favor.
The fact that Medica II can be cast whenever is probably balanced by being able to cast Whispering Dawn without defocusing tank and the fact it costs no MP.