Exactly. It's about whose definition of "better" you use. Sony thought that a better picture would win out, and it did where that mattered: TV studios and video-journalists used Betamax until digital formats took over. For consumers, "better" meant cheaper tapes and longer run time.

JVC also licensed the VHS format to many manufacturers, so there was a lot of competition on recorders, further driving the price of ownership down. I don't recall anyone ever selling Betamax other than Sony.

Edit: JVC actually released VHS as an open standard, not a license, per Wikipedia.

Pro TV used Betacam, not Betamax. Same physical tape, but four instead of two tape heads and a much faster tape speed.