TwoSix
Everyone's literal second-favorite poster
That might work OK in older games, but healing spells aren't efficient enough to justify the expenditure in 5e. I'd rather see my cleric using spirit guardians than healing someone for 3d8+4.We have a saying here: "Cures are better as hit points in the recipient than they are as spells in the Cleric".
I'd say use the magical healing first. Why? Because using one's hit dice is something anyone can do, and thus those hit dice are better kept in reserve for situations where there is no healer, or the healer is out of juice.
There are certainly counterexamples, of course, prayer of healing and aura of vitality are excellent out of combat heals. I generally find one good use of those and then spending hit die to top off is generally the best result.
Running out of spells completely is generally an indicator that the party is overextended and needs to pull back; you really shouldn't be reaching that point until you've expended nearly all else of your non-consumable resources. Save consumables for the real emergencies.