Something that I continually see references too, is that VHS won out over the allegedly superior Beta format. It's a fallacy, though. Neither are really superior to each other, they're both mostly the same. And in a number of important ways, mostly related to tape speed, VHS is better.
NB: This page discusses the situation in Australia, which used different tape speeds than America for both formats (the standard speed allowing about three hours of recording), and both VCR types came out here a lot later (we, also, didn't have colour television until 1975, and domestic VCRs until the 1980s).
Beta has a slower tape speed, so the linear sound track(s) are worse (which for a long time, were the only type of sound tracks on any home video tape system), any tape dropouts lose a more significant chunk of the signal, and the video tracks are closer together (allowing more crosstalk between them).
The different methods of wrapping the tape around heads can be used by either system, it's merely a mechanical method. So neither the Beta nor VHS tape recording system can really claim that their wrap is better than the other (the wrap method is a separate issue than the video tape standard). Though the type of wrap typically used on Beta machines is supposed to be less stressful to the tape, even if it's slower to thread up, and hauls more tape out of the cassette to do so (which, if it mangles, mangles more tape wrapped around the head; compared to the small amount of tape that VHS draws directly toward the head drum).
The old method of always keeping the tape wrapped around the heads, for Beta, had the advantage that it was quicker to go between fast winding and playback (while trying to find something), but did mean that the heads wore out a lot quicker (as you rewound a tape it was dragged over the heads for the entire time, even if it didn't need to be). Though the idea of keeping the tape always wrapped around the head, is not exclusive to Beta, nor does Beta have to do it that way.
Professional BetaCAM has nothing to do with the home Beta format, other than a similar-looking cassette. BetaCAM is not a proof that Beta was better, it's merely a development by the same company (Sony). There's a lot of technical differences between them: The type of tape, the tape speed (about ten times faster for BetaCAM), the method of recording the audio and video signals, just to mention the general differences.