So, the parameters are Price and Quality.
With those two in mine, defining what better is...
... then neither is actually better. It all would depend on what was on sale and what was available to you.
If you want to use your Western Digital product as an example, you can purchase the same exact hard drive separately, without an external casing. This means the only thing to consider the price of and quality of is the USB to SATA converter. What about the price of the hard drive? I'll get back to that.
Now... if you purchase the USB to SATA converter as part of an external case, yes... there are some that are better than others... but on the other side of that coin the PRICE of these is not always the best determining factor as to which is better. The oldest USB to SATA converter that I own, is part of a 2.5" external case that I purchased years ago for $5. It is not a recognized brand name. It has outlasted newer ones and ones supplied with WD external enclosures, and has been in regular use. However... unless you purchase the USB enclosure or converter WITH the hard drive, you must now factor in the shipping/driving (gas + time) into the cost of the part. If you are buying online, chances are you are getting both the drive and the enclosure shipped to you. If you buy them separately, then the individual shipping charges on each is most likely going to make the total for the purchase MORE than what it would cost for a pre-assembled external drive.
Now... remember, we started with the premise that the hard drive itself would be the same WD product. I brought up shipping... and once you factor that into the equation, your two parameters of Price and Quality have been addressed to show that you can find a pre-assembled product with a WD drive that will cost you less and provide quality usage for the lifetime you expect from it... and you can buy the parts and assemble one yourself that can cost the same and provide the same. It all depends on where you shop, and what deals you find.
Of course, if you widen the parameters, this changes the equation.
For example. Is dust a factor? Most WD external drives (the 3.5") have vents that allow a large amount of dust inside the unit, where many external enclosures don't have these vents. Are the construction materials a factor? Most pre-assembled external drives are made of plastic, where you can find empty external enclosures made of aluminum. We also cannot forget the Ease of Assembly. It can be a pain in the BUTT to get a pre-assembled external drive enclosure apart, should the USB to SATA converter fail... where a do-it-yourself kit can allow you to use that external enclosure as a drive testing kit (should you ever find yourself having to pull data from a different drive).