Peter,
As Rock Head noted, it was sound quality. Also, in the 1950s and '60s, before Ray Dolby introduced Dolby Noise Reduction for the cassette tape medium, if you wanted to record high-fidelity music at home or in live venues, it was open-reel or nothing.
Back then, cassette recorders were suitable only for dictation, strictly low-grade, low-fi.
Reel-to-reel also had lots of advantages over vinyl. No problems with "rumble" (the sound of the turntable belt/motor mechanism), much less flutter as long as you recorded at 7.5 or 15 inches per second (ips) and generally excellent frequency response from 25 or 30 Hz to 15 kHz or more. Plus tape noise was low enough that you didn't need noise reduction. You can still hear residual tape hiss on old recordings transferred to CD that haven't been processed with noise-gating and other noise filtering.
The distortion/overload character of open-reel was also very forgiving and generous, far better than cassette machines that came along later on.
So you could exceed the theoretical maximum recording level by as much as 6 to 10 dB before distortion became audible, hence you could record a surprisingly wide dynamic range. And the analog distortion with open reel was very different than say, a phono cartridge beginning to mistrack with highly modulated (loud) music passages. With vinyl that becomes much worse as the cartridge approaches the center of the disc and the sound gets really nasty and congested on loud passages.
None of that happened with open-reel. Any serious audiophile in the '50s, '60s, and '70s owned an open-reel machine.
Plus it was fun watching those big reels rotate and the big VU meters (record-level meters). I love spotting big open-reel machines in the background of Hollywood movies from that era that used "swinging bachelor" pads as locations.
Regards,
