The film base thickness for the same film is less for the 120 version compared to the 135 version. See Tri-X - the 120 base film thickness is 3.9mm vas. 5 mm for the 135 version. There is probably some minor refraction effect that causes a difference in negative and print quality.
This is the key, its the base density (as in densitometer). The film base for 120 is <50% that of 135. In other words, how transparent an unexposed piece of film is.
Take 2 pieces of unexposed film, one 120, one 135. Run a densitometer check on each (or you could scan them). The 135 will be at least 50% 'denser" = darker than the 120. This means you have to push that much more light through the 135 to achieve the same print exposure as 120. In short, the 120 is much easier to print.
You can compensate for the denser negatives by overexposing your 135. One of the best and most reliable method for getting good negatives and prints was given by Fred Picker's book 'The Fine Print.' Essentially, you need to determine your effective film speed using the film and developer combination you plan to use.
I learned and used this system in the early 90s when I was in college and ran the darkroom for a professional portrait photographer. I'm not bagging, but when I finally took a photo elective for fun late in my college career I ended up teaching a couple of the instructors how to print fine B&W. This system works and, most importantly, is reproducible.
A cheap and easy substitute for doing the test is to overexpose your negatives by 1/2-1 stop. Its very tough to really blow the highlights in B&W negative film, so you should be ok. Since the entire negative will be more dense your print exposures will be longer, but you should retain all of the tonality of 120, albeit with a little more work.
Good luck.