In a way there's a few factors to consider in the realm of heavy mana vs heavy mana regen.
The biggest one is the initial lack of AP and CDR that going with an early tear+ROA gets you.
The other really big one is whether you can stack the tear well enough, and whether you have other core items you need to finish before upgrading the tear (Viktor for instance, seems to work pretty nicely with tear seeing as how his hex core gives a decent amount of mana, but he's not able to spam quickly enough after getting tear and needs to sink a good 1000 gold into the first hex core upgrade before he can think of finishing a Rod of Ages, much less archangel's staff). Sometimes stronger core items (like sheen/lich bane) takes presedence or the champion just doesn't spam spells regularily enough for the Archangel's staff to graduate into a full 120+AP item in good time.
And then there's of course how well use you can make of the mana otherwise, and what other items you're building.
If you can get your AA's fully charged into a Seraph's Embrace by the end of the mid-game, then you'll be sitting on a vast quantity of mana, only 50% base less than Morellonomicon, a 120+AP item, decent amounts of health regen if you pick up the utility masteries needed and a cool little bit of utility from that shield.
But if you take too long to get it to AA's in the first place, or if the regen isn't enough (remember to get an
for all the mana regen you'll ever need), or if you need the CDR and have problems getting it elsewhere, or if the AP/MR you get from the components of Athene's/Morellonomicon could make or break your situation, then the investment might be too long term to be effective.
Lastly, on a game-to-game basis. Both RoA and AA's have very heavy build paths, meaning you usually can only get a new full component at 800 gold or more. Compared to Athene's/Morellonomicon where each component costs no more than 500 and is usually very useful to sit on by itself. It'll be a lot easier to go for tear->AA's/RoA in a game where you're getting good farm and manage to stay in lane a long time without backing, than one where you get zoned off from some CS here and there, or have to back frequently for whatever reason. Simply because you can always manage enough gold for a part of
or
's build paths while
and
both require
which costs 860 gold, which can be surprisingly high at times.