I can't find anything out there that compares the important functionality of hearing aids. So here's my inexpert opinion between these three.
I had Audible hearing aids for the last 5 years until they broke. So this is comparing to the Audible as they were 5 years ago. I then went to CostCo (best prices by far for hearing aids!) and got the Rexton. I tried them for 2 months and they sucked, so I then returned them (in Colorado you can return for a full refund withing 180 days of purchase) and got the Phillips.
Price: Phillips & Rexton are $1,800.00. The Audible you get from one of their approved audiologists and they tend to be $6,000.00
Quality of the sound: Phillips is the best. I can tell the difference from Audible, but barely. And Rexton is slightly worse than Audible.
Feedback: Phillips is the best, I really have to work at it waving my hand all over the place to sometimes (rarely) get feedback. Audible would regularly give feedback if I put my hands close but otherwise was usually ok (sometimes it would start doing it and I had to move the dome around). The Rexton would cause feedback a fair amount of the time.
Note: For the Rexton they tried molded ear plugs - those were awful. It was like listening inside an echoey cave.
Comfort: The Phillips are wonderful. I don't even feel them in my ear and at the end of they day, barely any pain from being there all day. The Audible & Rexton hurt as the day goes on. Sometimes I have to take them out after 6+ hours.
Direct connection to iPhone: The Phillips sucks. At first I couldn't even hear and they had to call Phillips tech support to learn how to increase the phone volume. It's still pretty quiet and sounds real tinny. Like a speaker in an old time drive in movie. The Audible & Rexton are both really good on this.
Power up/down sound: Audible & Phillips are both good. Very distinctive sound, good volume. The Rexton is awful, so quiet almost can't hear it.
iPhone app: Audible & Phillips have good apps. The Rexton app is embarrassingly bad.