Purple, some of the biggest hits reported by most media outlets to the MDXes reliability include questionable longevity of the electronics in the vehicle, namely the infotainment. But our small sample here hasn't really shown many infotainment unit reliability issues, rather that it's sluggish and cumbersome to use.
The 6 speed MDXes 2014-2015 has transmission juddering issues, which turned out to be an unforeseen early fluid failure issue due to heat causing a flutter in the torque converter. Acura is addressing this by a software update to the transmission to kept temperatures, but we're not sure what that means for performance exactly. Coming from having owned Hondas since the 90s, I do have apprehensions about the in-house transmissions (like their 5 speed...), but it looks like at least Honda is actively addressing the issue (they will change out your transmission fluid for free if you have the judder until the software fix is released).
The 2016s with the ZF 9 speed haven't really presented any reliability issues, rather awkward programming causing usage issues, especially during low speed. But Acura released a software update there too, which made many of us happy. Other than that, the MDXes problems seem to lie with fit and finish issues, rattles, and body panel alignments. Start-stop issues seem to be few and only affect Advance models.
All-in-all, not really much having to do with reliability aside from the transmission in the 2014-2015 models. If anything, your Odyssey becoming a rattle trap is pretty telling of Honda's (and Acura's) build quality issues with the Alabama plant (which builds both the Odyssey and the MDX, and now I believe the Ridgeline) and may be a sign of what is to come with the MDX (mine develops rattles, and Acura/Honda's stance is that this is normal with age, so live with it).
Which brings me to Emmet's point, and it is a very good one. The dealer experience with Acura is going to be pretty much just like a Honda dealer, albeit a bit more pretty and less flashy blue. If you find a good Service Advisor who doesn't use "it's normal" on you, you're in luck. But the turnover rate of SAs is high, so keep that in mind. I am in agreement that the dealership experience with Acura is pretty poor for a brand that markets itself as "luxury" and Infiniti has indeed treated me better as well in the past. A lot of it is appearances, but at the very least they don't try to shoot you down right when you bring up an issue. For example, in order to diagnose an issue with most Acura dealers, you will need to drive and show a tech the problem. This means if you ever have an intermittent issue, especially a temperature sensitive one, you may never get it resolved because the problem may not present with the dealer if their road conditions are different or if you are forced to demonstrate to a tech only at the beginning of their shifts at around 7am (this is a problem I have with all but one of my regional dealers, so it tells me this is a process of the brand). I understand why they do it, as they need to be able to know how to duplicate the issue, but even if you've shown them a video of it, they won't do anything about it until you can show them while driving. Acura Client Relations is pretty useless because they just follow what the dealership says.
Most of the issues I've seen cited and from being told by my buddy with a 2014 QX60 were with the transmission shuddering and some with the infotainment. The CVT transmission issues were pretty high in the 2014s, less in the 2015s but still significant, and fewer for the 2016s, but they still exist. No word really on the 2017s. Many seem to have involved outright transmission replacements as well (this is from my review of forums, Edmunds, and Consumer Affairs back when I was looking at the QX60). The infotainment system issues did not seem to be reliability issues either (much like the MDX), but more just bugs or usage issues (and mostly with the entertainment options). You may experience rattles early on as well, especially the dash area, so just keep watch for that while you drive one.
From personal experience with my buddy's QX60, he has had most of his issues resolved by the dealer, including transmission replacements. Rattles we kind of deal with if we can. The initial warranty is long enough at 4/60 that I don't think you will have much issues getting things fixed. It's just a matter of going back to the dealer to get them fixed (and it may be just the dealer we use that causes some of the repeat visits). After repairs/replacements though, things tend to be fine. He also had some problems with the electrical systems and some engine bay components, but again, those were dealt with over numerous trips.
Having dealt a few Nissan family products (and JATCO, the transmission manufacturer, with both ATs and CVTs) and from being with my buddy on quite a few of his QX60 appointments, I may be more jaded than others and is probably where my "may drive you nuts" comment sprouted from but more so that you will probably need to repeat visits rather than having many different issues. To be fair, the 2014 MDX was probably just as problematic for some (not all, like mdxstang has had a good experience), albeit not with the transmission but the infotainment. So it depends on your level of tolerance with various issues, dealership experience (we have switched a few times), and how the brand assists (Infiniti's customer relations is bit more accepting of cases vs Acura's stance of dealership makes all technical rulings).
The 16 Pilot actually turned out to be surprisingly quiet when I drove it about two or three months ago. I honestly don't remember thinking it was much louder than the MDX. I've been in older generation Pilots and those were definitely loud, practically Odyssey level loud because of the big rear hatch section. I was kind of jealous of the newer infotainment system (even more so now that the 17 version has carplay and android auto), but it does have its share of bugs as well according to Supertech, who used to visit here, and my neighbor, who bought the 16 Pilot after trying my MDX. Will it develop rattles and squeaks? Probably, but I should tell you stories about my 11 Genesis (caused by broken chassis welds resulting from... just driving.. Hyundai kept fixing it over 5 years) being louder than an 05 Subaru wagon that I still have (pretty solid in rattles department actually even after 11 years, but the rear hatch section just flexes). So far, the 16 MDX is ok and the dealer has resolved almost all of my issues except two noises. It has had more rattles than I would have expected for a new car, but they were all easy to resolve as long as the dealer was willing to do it (that's my main problem, they always come at me with not knowing how to resolve it to my satisfaction).
Ok enough of my novels. Go drive them both and see which one you like better.