I have to agree with @nuan88 on the mobile site comment. Unless the mobile version of your website is running something similar to AMP, this is probably not the best route to take.
Back on topic: I suppose the best way to think through this issue is essentially hosting multiple sites in one instance of MODX, right? You want one folder for the desktop site, another for the mobile, each with their own domain; or in this case, one with a sub-domain.
All that said, I don’t think you will need another install of MODX. Take a peek here once.
One major part that you might be missing is the manipulation of the htaccess file - maybe the mapping of the domains too.
Are you referring to users load time maybe? If so, this is technically true. Loading a website made for all devices onto a phone via something like Bootstrap would slow down the user. They would be loading extra crap they don’t technically need. Again, if you planned on having a stripped-down version of your site for mobile (like AMP), this could be a significant difference in loading time for the user. But, providing a wholesome experience (similar to the desktop) for users on a separate stripped-down mobile site is very difficult. And think, people’s phones and internet connections are getting faster every day!
Maybe the next project
–When you have some free time, I would play around with Bootstrap, it’s a lot of fun to just throw CSS classes everywhere!! It can be intimidating. Let me know if you have any questions.