I haven't gotten to spend anywhere close to the amount of time I want with Dark Ages, but I've played quite a bit with Catacombs. It seems really bad, to be honest, and like it really has little to no niche. Like it seems as weak as Explorer.
3 Situations
No trash - Catacombs is bad in notrash because you can't use the clause, so it's just an improved Smithy. You can play it as a big money terminal, but after all our expansions there's fewer and fewer big money terminal boards, and you usually can find a better terminal than Catacombs too.
Trash for no benefit - You don't want Catacombs at all because now you don't need to sift, your deck doesn't have many bad cards to discard off the top. The when trashed clause is still nearly useless, except for a stray 1 VP in some corner cases.
Trash for benefit - Ok, now you can use the clause, sure. But trash for benefit hits Estates, so it doesn't make much sense to play BM Catacombs. Estates were the only thing you were dumping off the top besides other terminals (Coppers are not bad for dead draw), so now the difference between Catacombs and Smithy is diminished even further.
So you say, ok, well I'll use the trash for benefit on Estates and then use Catacombs as an engine card, and I can dump Coppers off the top because now Coppers are bad. And that's the most common use I can see. But I'm rather concerned that even after you have trash for benefit and only trash for benefit, and you want an engine, some stars still have to align, because Catacombs is not at the engine-support-card cost. It's at the engine-premiere-effect cost, 5$. If the reason you want to build an engine on that board is Highway, then 5$ purchases are Highways, if your motivation is Torturer, that's what your getting. And so on. Bridge is a notable exception.
If there is no powerful 5$ card that is making you all excited about your engine, and you want play a "First Game" style engine, then Catacombs is an expensive Smithy, because the "First Game" deck draws all of its cards, sifting is irrelevant. Ok, not totally irrelevant, it slightly decreases the odds you fizzle after the first Village into Catacombs, but mostly irrelevant.
I compare it to Explorer because it seems a similar quality BM terminal, and because it seems like it's main saving grace is alt VP, and even then it's tough. Alt VP amps up both Explorer and Catacomb's quality as a BM+X terminal. So Silk Road, Gardens, and Feodum, those could work. Explorer Gardens definitely find boards it cannot dominate though and I think Catacombs would have a similar difficulty in consistently fulfilling the niche.