It all depends on the terrain you are riding in.
The big fashion now days is to ride with a tight flank cinch, placed back behind the swell of the belly along with a cinch hobble to the center of the main cinch. If you have a short coupled john mule and that flank cinch gets too close to the sheath ,things can get western real quick.The other thing is that if the mule has kind of a hay belly and you take him out to a days work in rough country,that hay belly gets worked off quick and that tight flank cinch you was depending on is now too loose to do any good.Yea,you can always get off and take it up some more,but what if you don't notice it.
The crupper vs the britching is an age old discussion.It is more a personal preference.However I think the crupper puts too much pressure on the base of the tail when going down steep grades and there is more of a chance of soring up a mule by not having it adjusted properly.
I believe the britching provides a more stable saddle and one can ride with a bit looser cinch and get more miles out the mule.
One only has to have their saddle ride up on a mules neck and the rider goes over the mule's head or have the bars impinge on the scapula to learn a little bit of precaution goes along ways.Don't depend on someone saying you don't need a particular piece of tack on a mule. It all has a function and has to be adjusted properly
Here is a website that gives a lot of info on saddle fit, tack ,etc for mules.When the page opens up,select the" Helpful Articles " in the green bar across the tophttp://www.albertadonkeyandmule.com/
As for the saddle fit,some mules require a mule barred saddle ,some don't. Not all mule barred saddles will fit all mules. The mule's back is straighter from front to back than a horse and horse barred saddles usually have to much rock on them to fit well. The saddle needs to sit back 3-4 " further than where it sits on a horse,and the cinch must be about hands width in back of the armpit,or you will get cinch galls.A saddle set too far forward will cause the bars to rub the top of the scapula as the mule walks because the mule's shoulder movement is different than a horse . Short rides won't tell you anything,