Ours turned all mule quite some time ago. I think at the time, the most compelling reason was a bad back. Because a 14h mule (all the higher than I carry to lift gear) will generally out pack a similar sized horse, and most any mule will generally be a smoother ride than most any horse at pretty much any gait. And also because as stated above mules generally, eat and drink less in both quantity and quality, probably the not as pressing in ID, but down here in the desert SW, it's a worthy consideration.
But the most important word in all of that IMHO is 'generally' because mules... and horses, for that matter, come in so many flavors that you really need to compare individuals examples to have a very meaningful comparison. Out of our current half dozen, even though they're all mules, they're all incredibly unique.
A couple of mule cliff notes;
If you navigate rocky, technical, single tracks, watch a good mule do this sometime. They are head down, looking at where their foot is going. Most horses are looking out ahead at the trail.
For those with less or no equine experience, it is infinitely easier to find anything 'horse' than 'mule'. Take a vet or farrier, for example, because a new owner probably shouldn't be trimming, shoeing, or doctoring their own. Many 'horse' farriers won't touch a mule, and most would ruin their feet if they did. They are not horse feet. They need to be stood up.
Also as pointed out above, mules mature slower, but that's in every facet. Not only do their knees close slower, but their minds mature slower as well. Adolescent age doesn't go away as quickly. A mule can be well trained at 3-4, and do all the cool arena stuff, but (s)he'll still do goofy colt stuff at 7-8 in the sticks. Meaning a beginner rider really needs a more seasoned mule, lest they be left afoot when a bush turns into a boogeyman. Truly bombproof usually doesn't appear until 12-13. This doesn't mean they can't be ridden or trained to do spectacular things at a young age. It just means their confidence is slower in maturing, so until then, it's going to be heavily dependent on your confidence.
As stated above, a mule is going to have to 'accept' you as lead, which is an exercise in building trust. But when (s)he does, they're also going to 'expect' that role of you, and consequently, anyone you allow to handle them. Asking someone low on confidence to handle a younger mule who is looking at them to be the leader is a wreck looking for a place to happen. This is true no matter their prior equine experience, I have watched horseman, farriers and vets have situations snowball, just because the mule knew they were concerned (read; scared), and consequently there must be something they should be watchy about as well. The old adage green on green = black and blue, was never more true than on a mule.
As far as sleezy horse (mule) traders goes, well... I guess there are slobs in all walks of life, and certainly horse traders peddling mules are not immune, but my experience has been that like many things in life, most good mules sell by word of mouth, with no salesmanship involved. You can spend a pretty penny at any one of a number of mule auctions on a dolled up, aced up, watchy wrek looking for a place to happen, or conversely a wore out park mule dead head... best advice here for someone shopping with less mule experience would be to find a mule mentor that shares the same mission scope and lifestyle with their mules and make friends. If you're not making your own, good mules will be harder to find than good horses because there are less of them out there. Conversely, with no inbreeding available, it's my opinion that there are probably fewer bad mules out there than bad horses as well.
Here's a good one to contemplate:
Turning the generalizations around to the owner, it is very easy, maybe even common for a horse owner to be an arse, personality wise, and still be successful in other aspects of life. A mule just won't put up with much bullshizz. In fact, BS is IMHO what makes bad mules. An asshat will soon rid himself of mules or fix his poor attitude (at least around his stock). I find my own chronic case of assholiosis vastly improves with more time spent around ours.
If you've been to Bishop, Clark, or any of the other big mule shin digs, you've seen all kinds of mules doing all kinds of things. In fact, a trip to Bishop should be required reading for people considering mules, but I digress...
So I guess circling back to the OP, my answer would be either... horse or mule, just make them one's with appropriate lines and temperament for the mission. There is so much overlap that either one selected well will do your job well. The real differences are idiosyncrasies that come down to personalities of both keeper and beast an take a well-rounded horseman to appreciate, but a well-rounded horseman will bring the best out in either and do well. Well rounded being key, because the average horseman is not a muleman.
Did I mention mine are all mules?
Take care,
Rob