Question about JR and private line usage

I'm just interested in the market share between public and private train lines. Would most people be serviced by JR for getting from home to work and back?

What are you asking?

Note that JR is neither a company, nor public. It is a loose consortium of many private companies, although in common usage companies which are not members of JR are still referred to as "private".

It depends on the city.
But I am afraid I cannot easily find the data.

In Tokyo, I think it is around 50-50.

In Osaka and Nagoya, I think JR is the minority.

http://www.mlit.go.jp/k-toukei/saisintoukei.html
鉄道輸送統計調査 is so. (Open PDF or EXCEL)
定期 means "commter pass" users but not only for worker include school students.
定期外 means "temporary" passengers.

English page's data is already old.
http://www.mlit.go.jp/k-toukei/transportation_statistics.html
http://www.mlit.go.jp/en/statistics/white-paper-mlit-index.html
Also not enough as data details and contents diffrerent mostly for different readers.
JP : http://www.mlit.go.jp/tetudo/index.html
EN : http://www.mlit.go.jp/en/tetudo/index.html

MLIT?
http://www.mlit.go.jp/common/000026153.pdf
https://en.wikipedia.org/wiki/Ministry_of_Land,_Infrastructure,_Transp...

This is not MILT's but usefull published by official(mainly railway companies) released data based.
http://www.geocities.jp/l00az/

However,comparing JR or NOT is meaningless bc quite not equal conditions.
Competing/Conflict zone are not so many than you think only some major urban cities and airports access.

For many people, being serviced by JR for getting from home to work and back is their best or only option, if that's what you're asking.

To begin with, do you want to compare public and private? Or do you want to compare JR and non-JR? And why?

All JR companies are private. Meanwhile, there are many public railway companies, and they are not JR.

This may help you understand what JR actually is.

https://en.wikipedia.org/wiki/Japan_Railways_Group