Amex seems to have killed their bonus mall. No one knows for certain if it is ever coming back at this stage since there have been words from CS on both sides of that fence.
I don't think Amex ever had a way to earn extra cashback online, just MR points (though I could be wrong). I've looked at Chase and it was alright. Lots of people seem to like Discover's online mall. I just do most of my online shopping at Amazon though.
go to evreward to check. Most of the time, Chase is the best, since each point is worth 2 cents for me.
Citi forward probably. It's 5% points back all the time. They have recently improved their Thankyou points redemption for Citi Forward card holders, so it's 1:1 for almost all the brands they have there.
But I just buy small gift cards (less than 1 dollar) using Chase Freedom (10/10) and then put them into my account. So you get 10 points everytime you make a transaction. People usually get too greedy and buy thousands of 15cents gift cards all at once -- Chase usually just closes your account. But I think doing several a day (of varying amounts) would be reasonable and I don't think will get much attention from Chase.
The only 2 good cards for amazon I know of are the citi forward, and the amazon visa card. (the two best afaik at least)
The USAA amll is pretty good, varying points multiplier depending on the merchant. Some places offer up up to 6x points. Tons of big retailers. I find myself only shopping at places that are part of the USAA mall, addicted to earning points.