Ok (for checking) interest rates. Haven't used them for billing yet (I don't think they do proper e-billing, instead they'll send a check for you). I won't say 0 fees. They have fees (like most banks) if you use the card outside the US, but that's why I have my two travel credit cards (AMEX and Visa because not everyone accepts the former, but it gives me the best rewards).
The budgeting is neat, though they added a new "expense" budgeting thing that I haven't quite figured out yet. Previously they had "goals" which you'd set up one at a time, burn through. Like "August Lunch Money" with $200 in the account by 31 August (give me a little to spend each day, not all at once). Now you can make a "Lunch Money" expense that'll get replenished each month, but it's only been around for a couple weeks and I think I set it up wrong.
They still have goals, which are effectively digital envelopes. But if you use other budgeting tools it's somewhat redundant.
Deposits happen quickly, typically within 24 hours of sending the money from my primary checking account (I set up Simple to try and bring some more financial discipline to my life, not to be my sole account).
They don't offer any better API access than anyone else. The joint accounts are neat (3 accounts, one for each person and one shared). But only works for US citizens, my fiancee will have her green card but not qualify until they change that policy or she becomes a citizen (late next decade). Instant transfers between other Simple account holders, which is nice if you have other people you know who use it but the same is true for most banks (near instant intrabank transfers).
Responsive customer service. I've had maybe 3 or 4 issues or questions over the years, and I've always gotten a response (conducted over email) within 24 hours, probably faster but I only check my home email a couple times a day.