Might best be asked/cussed/discussed in Comparisons and Advocacy ...
https://moodle.org/mod/forum/view.php?id=2784

but ... since this is here in General Help .... so I'll begin with an observation (over years using Open Source) and some comments ...

The request is to make a Biz case for Moodle based upon tech features? ... so ...

Free isn't Free.  From your profile and from other postings in forums am guessing you are a "Learning Technology Person' but not highly technical ... and frustrated easily when an 'expert' doesn't respond quickly and with exactly what answers you sought.   Been with an MP (hosting with an MP would be one of the first suggestions the 'Moodle Faithful' would make to you) ... but are no longer?   Seeking to move to robust Amazon set up?

Been my experience ... personal as well as working with K12 and Corps as well as individuals ... that many don't have the inclination to put on 'other hats' as needed.   By that I mean command line and some DB admin ... Moodle isn't just the successful installation of a site ... but tip of an iceburg.    Are you willing to take a dive into what might be 'cold waters'?

0$ cost really isn't true ... besides ... appears you are not the primary decision maker or you wouldn't be asking for such advice.   So who are the decision makers (DM's) in your entity?   Do you think those DM's are of the mind set where the only thing is the bottom line of cost?   Who are your entities "power players"?

Are there 'birds of a feather' in your entity that are 'influencers'?

Not nay saying ... not trying to discourage you ... go forth ... just be prepared for what might be a battle, a dive into cold waters, and fatigue treading water ... until you find ways to do battle, warm the water by treading without going under!

'spirit of sharing', Ken

Ken has made some excellent points, and I am glad that he provided the link to "advocacy."  Some folks around here know that I have been helpful, not helpful, and a little vocal here on Moodle.org because I have gained some experience with Canvas because my university uses it, and that my university would like me to use it.

What you say is true.

Ken mentions cost, and since your school apparently has purchased Canvas (or soon to purchase) then you should know what your school is willing to pay, and this then provides a good idea of what your school would be willing pay for Moodle, either by hiring competent people (or consultants) to help, or by using a Moodle Partner.

Making a "business case" can be difficult.  Sure, the cost is one factor that is easy to see and compare.  The much more difficult factor is "quality."  What makes this even more difficult is that "quality runs deep," meaning that on the surface, all these LMSs seem to look the same.  It is only when you really get into each product and push them a little that one begins understanding the differences.  For example, the Canvas "forum" tool does not show threaded replies, it indents only the first level, and you lose track of who is saying what to whom.  This is a very serious flaw!  However, one might say "Canvas has a discussion feature, and so does Moodle... both products are the same."  I think you see what I mean.

Furthermore, you run into people who say "It is good enough for me.  Why do you need the feature of Moodle?"

On the other side of the equation, Moodle is really much more flexible and packed with features.  But this makes Moodle more "complex."  Canvas' strategy is to "keep it simple."  So, when Canvas users ask that they should be able to sort the list of students by more than just last name, such as by first name or last access date, Canvas seems to say "Sure, we could do this, but we won't because that makes our product more complex.  Sorting adds complexity."

Be aware that Canvas needs to "sell" their product, so their marketing staff will tell you things that are not always correct.  (Oh, being fair, maybe they would say "grey.")