People tend to cite 4k, but even that I don't believe, because if that were the case, you wouldn't see much (or any) improvement on a bluray between 35mm and 65mm, and yet, we do, a huge difference. The Master looks substantially better than any 35mm film on bluray, and even The Master has a few 35mm scenes, and the difference is noticeable immediately.
A lot of this depends on a multitude of things. Mainly, how good is the source print they are scanning from, how are they scanning the print (not all scanners are the same quality), who's overseeing the scan, how much time are they devoting to fixing it up, etc.
A well kept 35mm print that was shot on a good lens will get you around 20 good megapixels before it's too noisy. 1080p resolution is 2 megapixels, 4k is around 9 megapixels, 6k is 19 megapixels.......so yes, 35mm film can potentially give you an amazing image on 4k, let alone on blu ray.
You can have a 35mm film that was scanned from a bad/damaged print that looks like shit, then you can have one that was scanned from a well kept print that looks great, but both can turn out bad if the company doing the scan don't take the time to do it properly, cleaning it up, resorting it, color correcting, fixing damage spots, etc.
I mean look at Suspiria for instance, watch the new Synapse blu ray, it looks jaw droppingly breathtaking, even stacked up against brand-new movies that were shot digitally. They scanned the print at 4k and it took them over FOUR YEARS worth of work to do this, frame by frame, that's how much time/care they put into it, as well as getting help from the films cinematographer.
http://synapse-films.com/news/suspiria-comparison-pictures/
Many movies simply don't get that kind of care behind their releases, either neglect when the source print was stored which leads to damage of the source print, or they just scan the film "as is" without taking the time to do it properly and carefully when it comes to cleaning and restoring it the best they can with the source they are scanning from.
Hell look at the 4k release of Terminator 2, it was a disaster, one of the WORST 4k releases, even the blu ray looks better because they dnr'd the hell out the 4k release and people look like wax with all the detail scrubbed away.
Now look at the 4k release of Blade Runner, simply amazing to watch at 4k.
This is a good short video showing the process of film restoration and what they go through (from Criterion)
https://vimeo.com/84135659