Both these cards are pretty easy to get, and I have both. It's nice to have both because the Diners is a better card, but there are still many laces that don't take it. So I use Diners when I can, and a variety of other cards when I can't. But Diners is certainly my favorite mileage earning card overall, for the following reasons: Last 3 years they've had a double conversion "sale" where you could convert the DC points to British Air miles at 2 points for every dollars spent. This is a great return! In 1999, they also did this once with Delta. So at each opportunity I transfer all DC points into one of these programs. Also they have the best customer service by far in the industry, best rental car insurance coverage, some good special offers sometimes, etc.
The Citibank AAdvantage is also a good card. Thye have had a promo last 6 months for a Click Citi card (find old threads on FT) that gave 2 miles for every dollar. This promo expires this month, but perhpas they shall repeat it?
If you want the Diners Club, I'd be happy if you'd use my referral. And Diners Club gives you 24,000 points for a first year bonus just for paying the $80 annual fee and using the card once a month. So this is well worth it I think. Good luck.