The problem with external enclosures is heat. Standard internal drives expect some ventilation, while external enclosures often seal the drive in with no forced ventilation.
If you want an external drive, it would be better to get something like the WD Passport, because it is already engineered with the intention for it to be used externally. Also, these types of external drives, being targeted for external use, will probably be engineered to withstand more bumping around than a standard internal drive(stuffed in an enclosure).
Now as far as your question about whether the external drive, or your laptop's hard drive is more reliable, I don't think can really be accurately answered. The best thing to do is assume either will fail at any time, and take precautions to protect your data! The problem with hard drives and reliability is it is very difficult to quantify or measure, and manufacturers generally have no incentive to invest in significant improvements to reliability. They can offer better capacity, RPM, and latency, in an effort to increase sales. However, increasing reliability through design and QA will cost them extra money and increase drive costs, and it is not something quantifiable that they can use to market and increase sales. So from one drive to the next, it's really hard to know what to expect.
Very often when copying large files at the same time, they'd get corrupted along the way or give out errors. The simplest solutions is not to copy them all at once but there are a few things that can be done.
It could be a hardware issue, so you could check you memory sticks; it could be a bad RAM module. You could try out your RAM sticks, test them by switching them. Also, update your chipset.
You could enable the Write Caching option of your external HDD for better performance. This is usually the best performance choice for storage devices.
Access Device Manager, double click on Disk drives and then on your WD Elements, click on Policies, under the upper Removal policy section, select (dot) Better performance, if "Enable write caching on the device" is not checked, check it as well. Make sure that the "Turn off Windows write-cache buffer flushing on the device" is not checked, to prevent data loss, as your external drive doesn't have it's own power supply. Click OK and restart.
Make sure you always wait till all the files are copied and then always "Safely remove the hardware". It's possible that if you eject the WD external drive unsafely, that some of the copied files would be damaged.
You could also check if it's your external hard drive that's causing the issues. You could do it with the WD Data Lifeguard Diagnostic tool:
http://support.wdc.com/product/download.asp?groupid=810&lang=en
Or you could do it with the CHKDSK command. Connect your WD Elements, go to My Computer, right click on the drive, select Properties and then Tools and then Check now. From there choose the action you'd like to perform, including the option to fix file system errors and the recovery of damaged physical hard drive sectors. If both options are unchecked, the utility only reports problems found, if any, without fixing them.
I hope any of this will help you!
CK_WD
Official Representative of WD
Best Answer
This may be better treated as a comment, but too much detail for a comment.
A suggestion is to use Robocopy
Open Notepad and type the following, editing the source and destination path with your source and destination (please note)
if you want to copy all the subfolders then use the /E like:
Save the file as copy.bat and then run the script (double click it to run).
Let me know if you get the issue still.