In a CC game without chess engine assistance the CC champion would get destroyed by the OTB champion. However, people who play advanced chess are so good at operating chess engines that they have often beaten super GMs (who also had access to the engines, but were not so proficient in using them). Nowadays computers are so strong that is all boils down to who will squeeze the most out of the machine's capabilities.
P.S. That's why I don't like CC.
I am not at all convinced this is true and I wonder what evidence there is to support it -- IMO a strong, patient CC player (without an engine) is playing strong moves... I don't believe a strong (champion) CC player would "get destroyed" by anyone at CC -- that's the nature of strong CC chess... it tends to be pretty damn solid chess. I can't recall, but which world champion was it (maybe Tal?) who said -- "Perfection? I leave that to the CC players"
Is there any objective source of data regarding how CC champions have fared against World Champion caliber OTB opposition. Alekhine and Keres both played CC... I wonder, did they "destroy" their opponents in CC?
Do we have Alekhine or Keres' CC games preserved, surely they're around, but I don't think I've ever seen them.
I think such news are very common Robert:
http://www.chessbase.com/newsdetail.asp?newsid=2461
Where you can see that it's all about time and engine power: a team of two players <1700 + an ordinary engine defeated teams of GM's+engine. Knowledge is not important.
As for Berliner: he drew with Fischer when Bobby was only 14-15 and far from the top. Many other players defeated Fischer at that time. Anyway, I don't argue about Berliner's OTB strength. However, if he is such a great player, why everybody ignored his "proof" that 1. e4 is inferior to 1.d4?