You might consider asking this in /r/askscience since this is a technical question at its heart rather than an historical one.

Before digital, movies in theaters were mostly screened using 35mm film. This is an analog format so it is not directly comparable to a digital format like 1080p HD. By at least one estimate, 35mm film is comparable to a digital camera shooting anywhere between 7 megapixels and 20 megapixels. But in any case, it is quite possible and quite routine to take a 35mm master of a film and digitize it at 4K resolution and it will, indeed, include enough detail to be considered to be at full 4K resolution.

Safety copies would often be made at a 16mm format because the smaller reels were easier to store, but these were rarely meant for actual screening in theaters. Sometimes, though, safety copies are the only surviving prints of a movie, and at 16mm, the detail of the film is noticeably less than 4K or even 1080p format. If you pick up the latest reconstruction of the 1927 film "Metropolis" on Blu-Ray, for example, it is immediately evident which parts of the film were mastered from the full 35mm print and which parts came from the less-detailed 16mm print. (The 16mm was longer, so it was necessary to use in order to present the film as it was originally released to theaters.)

By the time TV came along in the early 1950s, Hollywood had begun to develop even larger formats than 35mm film, like 70mm film (CinemaScope, Panavision) or Cinerama to give an even more detailed viewing experience. When mastered from 70mm, a film can easily exceed the detail presented in the digital 4K resolution used in movie theaters and on Blu-Ray today.

The answer to your question, then, is that pre-VHS, movies in theaters were mostly shot and shown in the analog 35mm format, and for big budget releases, they would often be shot and shown in an even more detailed format such as 70mm film.

These formats are detailed enough to be digitized at 4K and appear to be in full "ultra HD" resolution.

That said, before the rise of multiplex movie theaters in the 1980s, the equipment at any given theater would be different. A theater's projector could be old and dirty, and some theaters did actually screen films at 16mm, so the detail would be somewhere better than standard definition but not as good as high definition. And if the theater was constructed so that the projector had to be placed too far away from the screen, then that would effect the quality of the visual presentation as well.

In short, any format used on the big screen in the analog days had the capability of looking better than standard definition, and any 35mm presentation or better (which would be most of them) had the capability of looking as good as the 4K ultra high definition format. But whether or not it actually lived up to those standards depended on the placement and quality of the projector, and the quality of the screen.

EDIT: Here is a source going through the typical theater formats used in the late 1960s. And this book details all the widescreen formats available during the analog era. For comparisons between analog and digital, you will need to look at sources from within the past 20 years, so I will leave it at that, but just know that 35mm or greater film is generally able to be digitized into full 4K resolution. Any of the more technical details, you might want to ask at /r/askscience or some other technical sub.