Citibank has made news recently because they have been sending out more credit card offers than there are adults in the US. As far as what their "best" is it would depend on what you are looking for. Simplicity and Platinum Select offer 0% balance transfers for 21 months, so if you are looking for a long term balance transfer those are the best. They offer Dividend
which gives 1% cash back on all purchases plus 5% bonus on items that change quarterly (such as gas, groceries, home improvement); the Forward card gives cash back on dining out and online at Amazon.com; the Thank You cards offer points towards different items or gift cards and the AAdvantage cards are for American Airline miles (different levels means different annual fees and bonus sign up offers). They also have the Hilton Honors Visa that earns points towards free hotel rooms although most agree that Amex's Hilton Honors is slightly better.
In terms of their ultimate "best" offer period it is their AAdvantage Executive World Elite MasterCard that carries a $495 annual fee and by the end of their year it should be offered with the EMV "Chip and PIN" feature that makes using cards in Europe a breeze.
I have three Citibank cards (one, my AT&T Universal, was issued by another bank that Citibank purchased) and I have been fairly happy with them. In my experience they go above and beyond to make a good cardholder happy such as giving CLI's, APR reductions and product changes. I recently received an email from them saying that they "were listening to customers comments and wishes" and they have guaranteed US customer service representatives when calling them amongst other things. The only issue I have had with them was last year when they decreased the credit line on my Dividend card by $2700 after a review of the account in which they "noticed" I was not utilizing my full credit line. At that point the account was 10 years old, I had a 790 FICO score and about 2% utilization and I always paid the account in full each month; no new accounts or inquiries.
I feel that because I started shopping at Wal-Mart they profiled me and reduced the credit line (but still left me with $9,000). Then, 4 months later they increased the limit on my AT&T card-which I might add I NEVER use and therefore NEVER use my full credit line. These banks must think we are morons! Other than that, I have only good things to say about them. Your Mileage May Vary (YMMV) of course.
My Citibank accounts were all opened using an Experian inquiry. Most banks use Experian as a general rule as it is widely regarded as being the most up-to-date.