Are there good reasons to believe that "enterprise" hardware is more reliable in practice?
Anecdotally, most desktops I used lived much longer than most servers I worked woth. I know a Compaq desktop that worked as a server for 11 years. Still does. One hardware failure in that entire time. (Power supply.) Could be a result of lower workload, but still...
There are superior aspects to the design of "enterprise" hardware (or rather, rack mounted server hardware) that have been mentioned by others: ECC RAM, redundant PSUs and HDDs, motherboard designs that (hopefully) are laid out for ideal airflow, etc.
Putting all of this aside though, the real secret to the superiority of hardware meant for the datacenter often comes down to the practice of binning. Manufacturers have different tolerances for the products they produce; hence why Intel has a million models of CPUs, Seagate produces so many different hard drives and Samsung sells DRAM chips to other vendors and makes their own DIMMs.
The products that perform the best are binned in the server-y bins, the others are moved down the list until they fit another bin. No manufacturer wants to discard parts if they can possibly avoid it.
Sometimes you're actually getting a deal, but a lot of the time you're just trading reliability for cost when you use lower binned items like desktop hard drives in a server environment. Sometimes that trade-off is worth it though.
Sure, but we're not speaking about overall system reliability. We're speaking about hardware dying. RAID will prevent data loss, but your actual disks might fail as often as something from vanilla PC.
ECC RAM will both work-around and warn you about the start of RAM failures before complete DIMM failure.
And sure, consumer drives have the same MTBF as enterprise drives in practice[1], but: when RAIDing consumer disks, make sure that you get models that immediately report read/write errors, instead of retrying, which is the main (or only, if SATA) difference between enterprise and consumer drives.
If you have a nice RAID setup, you DO NOT want a drive to retry a failed block read 15 times before reporting a problem, and causing latency: you want the failed read to be reported immediately, so your controller can pull the same block from a different disk, and start diagnosing possible faults.
