I would think IH would be better for mana efficiency if you're non-stop healing the tank than aegis would.
Yes - if pure heals-per-mana is your concern, IH beats Aegis until you get to very high levels of crit. Aegis is obviously crit-dependent and also relies somewhat on synergy with Rapture, making it scale with your mana pool and spellpower; whereas IH provides an essentially fixed discount.
Assume you have 1600 spellpower, 20K mana, and 25% crit (that includes Renewed Hope and Holy Specialization), with most of your points in Disc talents:
Greater Heal baseline (non-crit) will heal for about 7500 and cost 1236 mana. Rapture will return 402 of that (non-crit) regardless of whether we choose IH or DA, for a cost of 834 mana (without IH) or 649 (with 3/3 IH). On a crit, we hit the rapture cap and get back 500 mana, for costs of 736 and 551 respectively.
Now we can calculate the average heals-per-mana that IH has with GHeal: (0.75*7500 + 0.25*11250)/(0.75*649 + 0.25*551) = about 13.5.
With DA, we get two additional benefits: Rapture returns mana when the shield absorbs damage, and the shield itself may be counted as healing above and beyond what we already got. The mana returned will be 181, the shield is just 3375 extra healing: So (0.75*7500 + 0.25*14625)/(0.75*834 + 0.25*555) = about 12.1.
You can mess with the numbers some (for example, see what happens if we assume that crit overhealing goes to waste), but they don't change the basic result. If you push the crit percentage up to 35% and also assume that overheals go to waste (but the aegis obviously does not), then DA starts to look competitive in terms of heals per mana.
However, I think that unless you're really feeling mana-starved you would still want to switch to DA around 25% crit, just for the superior average throughput, which is substantial. It's probably about 7%, which translates to an extra global cooldown every twenty seconds to do more stuff (if spamming heals) or maybe even a chance for OO5SR regen (if there's a lull).