Is there any evidence of a benefit to distributing documents to students vs taking notes?
There is contradictory evidence I think on whether for the general student, providing materials is beneficial or not. 

For example, a study finding a benefit in providing notes:
Raver, S. A., &amp; Maydosz, A. S. (2010). Impact of the provision and timing of instructor-provided notes on university students’ learning. Active Learning in Higher Education, 11(3), 189–200. https://doi.org/10.1177/1469787410379682

A study finding that providing notes is detrimental:
Weatherly, J. N., Grabe, M., &amp; Arthur, E. I. L. (2003). Providing Introductory Psychology Students Access to Lecture Slides via Blackboard 5: A Negative Impact on Performance. Journal of Educational Technology Systems, 31(4), 463–474. https://doi.org/10.2190/KRW7-QHFY-AY3M-FFJC

Lots more on google scholar.

However, i think it is better established that providing notes is beneficial to those with various specific learning difficulties (SpLD) like dyslexia and dyspraxia (although I don't have the evidence to hand) and we are required to provide materials to this group of students. Given the large number of such students in a modern classroom, and the effort it would require to distribute materials to only this group, it is easy just to give it to everyone. 

I tend to provide my slides, before the lecture, but  - my slides contain little to no text, meaning some notes must be taken. I also draw a lot of diagrams during the lecture, that are represented as blank slides in the pre-lecture notes. 

After the lecture I provide the slides with the blanks filled in, and my speaker notes.