My two cents on the current candidates:
As for Burton, I thought he was good on PiR94, BUT I'm not sure he fits in on daytime Price. He has that booming voice, which is a plus, but, on the other hand he borders on stereotypical generic game show announcer voice, which could work for or against him.
Randy, on the other hand, is almost completely the opposite. Randy has the more friendly sounding voice (thus, more Rod-like), but at times can come off seeming a little bland, not that he's not enthusiastic, but he lacks that 'boom' that Burton brings to the table.
Fact is, I'm split, and it'll take a little getting used to either, I'm sure. Don't take my critiquing the wrong way, I feel both do a good job on the show, and either would make a good replacement. I used to do voiceovers and a live radio show, and even THAT isn't as easy as it seems, let alone what is probably the most coveted voice job around.
On a side note, good luck to you Randy, as I'm sure stepping to that podium Nov. 9 on a show to celebrate Bob's birthday, when your longtime friend is gone, will be somewhat difficult, but I'm sure all of us here support you to get through what I'm sure will be a difficult day.