Both have interesting features, being more secure and not normal scrypt coins. But which one, Darkcoin, or Vertcoin, should I put my hashing power to?
I think they both have excellent potential.
If you are really asking which one to mine, as in mine and dump, none of these 2 are very profitable (not the most profitable at least), so I would recommend you any other more profitable coin. If you still want one of these 2, then Darkcoin basically because your cards will consume much less electricity and the room won't get hot.
Now, if you are thinking about mine and hold, again mine any other more profitable coin, dump and buy VTC or DRK, personally I'm holding DRK because I believe it has more possibilities to have a real world use, a.k.a. a lot of demand, a.k.a. high price, it's not only about anonymity, it's about having a dev full time innovating and adding features.
Don't worry about premine, instamine, asic resistant ... just think which one has more possibilities to go 10x its current value. The reason why BTC has a high price is because it has a function outside the crypto world, DRK has one too, but I'm afraid VTC doesn't, only within the crypto world as "asic resistant" (which actually might not be desirable in the long term).