I use an assortment of billpay methods. MyCheckFree.com, my bank's online billpay, and certain OCs billpays on their websites.
I like MyCheckFree because it's like doing free wire transfers. The money comes outta my bank account on day X, and it's credited to the OC on that same day. No float. If I could do EVERYTHING with MyCheckFree, I would. It's bank agnostic, and in fact you can set up multiple bank accounts and pay select bills from select accounts. Downside is that an OC has to participate in MyCheckFree. Upside is a lot of CCs, utilities, et al. do participate and MyCheckFree customer service is superb--although I've rarely needed 'em. Also, I get to schedule when the money goes. I can pay 'em early, and decide how early. I schedule payments usually on the date of my Direct Deposit. I never really miss the money that way.
I tend to avoid letting the OC withdrawal from my account directly--mostly because I've had 'em screw it up more than once and I'm left fighting them to straighten it out, get penalties and fees removed, or get adverse TLs updated. If you've seen my GW letters, one of them is to GMAC because they transposed routing number on my check. That said, I do pay a couple of OCs via automatic draft, grudgingly.