There's no inherent difference between what you describe as a "desktop" vs a "portable" hard drive. The difference is in the drive and its enclosure, but there is nothing that determines whether an external drive is used with a desktop or as a portable drive.
All of these drives consist of a standard hard drive in an enclosure. The difference in weight is due to the enclosure, and whether a 3.5" or 2.5" drive is used. As performance improves on 2.5" drives, more of them are used for such purposes, because they are smaller and thus easier to transport.
The failure rates for 3.5" and 2.5" drives are comparable, but as a general rule, the price for a comparably-fast 3.5" drive will be less than that for a 2.5" drive. Also, many of the external enclosures for 3.5" drives include fans to keep the drive cooler, thus adding to the size and weight.
If I were after the best external drive possible, I'd buy the best enclosure, one that included some active cooling, and then put the best drive that I could afford into it. Most of the pre-packaged external drives don't use the fastest drives possible; if I cared about performance, I'd buy a faster drive with a longer MTBF (and associated warranty), especially because external drives do tend to get hot, shortening their life. Since the concern in the question seems to be focused around reliability, your best bet is to go to specific manufacturer data. Each drive will have a listed "mean time between failures" or MTBF (average amount of time the drive would run before breaking) and a manufacturer's warranty; a drive that has a 5-year warranty is obviously going to have better odds of lasting longer than one which has a typical 1-year warranty.
However, you'll also need to look at performance. 2.5" drives (the kind in laptops and in those little portable USB enclosures) come in speeds of 4200, 5400, and 7200 RPM; this speed will have a significant effect on performance. Desktop drives typically come in 5900, 7200, and 10,000RPM speeds.
There is a good, if slightly dated, analysis of these differences here: http://www.notebookreview.com/news/notebook-hard-drive-guide/
But whether or not an external drive contained a 3.5" disk or 2.5", and whether it was a "desktop" or "portable" drive, simply relies on the choices I make in how I intend to use it.
Here's an example of a big ol' 3.5" enclosure that has a large fan to keep it cool:
and here's a small one for a 2.5" drive, that you can tuck in your pocket:
the latter is just a bit smaller than a 3x5" index card, and less than 1/2" thick. There are all sorts of variations in between, too.