I've used online Bill Pay now for about ten years.
AND has it every improved over time.
My first experience with it was exceptionally painful. I was using a local bank, and admittedly, it was still early days for online banking. They were working with another firm that was offering the service for multiple small banks.
It was difficult getting the account established initially. They would require in-person, in-the-bank, verification of who you were before you could get your account unlocked. Your account would get locked if you didn't log in every two weeks, if you tried to change your password, but it had erred out (and didn't tell you it had erred out), or if you failed to change the password in the timelines they required (every 3 months).
Additionally, it was painful setting up a new payee and there were a few hiccups here and there where the payments weren't getting sent when they stated they would send them.
I moved out of the small town where the bank was located, and after a couple of more locked accounts where I had to actually drive 60 miles to present my face in-person, in-the-bank to get an online account unlocked, I switched to a larger financial institution. Bank-not-to-be-named as I actually work for it.
Online bill pay at the new national institution was extremely intuitive, easy to use, and prone to no errors that I can remember. If I wanted to change my password, I could easily do so and get very good visual indications if there were issues (which there weren't). Setting up accounts and payments were straight-forward and simplified.
I've since switched banks to another national institution (also-not-to-be-named as if I name one and not the other, it's highly likely you'll figure out the other) for reasons unrelated to the online bill pay.
BUT, I got the same exact positive experience. Online bill pay is smooth, fast to set up, easy to manage.
I've been talking to friends that bank locally and none of them use the online bill pay. A couple of them had tried to set it up, but had gotten frustrated by the process.
90% of the time, I try to support local businesses over big chains. My exception to the rule tends to run along the lines of price and/or support. If I could find a GOOD local bank or credit union with AWESOME online bill pay, I would switch to it. In the meantime, I think I'll stick with my current bank because 99% of my bill paying/banking transactions occur online at this time.