Both the 'X' and 'Ti' versions of those cards can be quite a bit more expensive than their slightly slower, but less expensive siblings, check some reviews and decide if the extra money is worth the extra performance for you.
If you're making this kind of expensive purchase warranty and service may be more important to you than cost, or noise, if that's the case EVGA win hands down if you're in the USA or Canada, XFX also offer an exceptionally long, lifetime warranty in some countries although their service has slipped over recent years.
Because it draws less power and produces less heat the GTX 780 is probably the better choice for cool and quiet overall and Nvidia do offer better AA options, PhysX, Shadowplay and, if it's of interest to you, Gsync.
With higher heat output the R9 290 demands good case ventilation and a top level cooler, Sapphire Tri-X, Sapphire Vapor-X, Asus Direct CU, MSI Lightning or Gigabyte Windforce are amongst the best but the Tri-X and Windforce is large, so choose your case with care to ensure such long (12") cards will fit. Biggest plusses fro AMD: Lower prices and more memory.
Given the funds, I'd go for a Direct CU II GTX780Ti in a heartbeat but a more realistic card for a single or even dual display would be the R9 290.