You may want to cross reference the current specs on the 2 HDs that came with the 2 MacBook pros. You can do this by checking a website like everymac.com, or simply taking off the bottom case on the MBP you just purchased. The maximum interface speed may vary. Not really an issue with physical compatibility- you may just be putting in an inferior HD.
http://www.everymac.com/systems/appl...drive-ssd.html
The one software issue you may encounter is if the external HD has an older OS X build than the current internal one that shipped with the laptop. Installing an HD with an older build should still work, but some functions on the laptop may be glitchy. My recommendation is that you install the external HD and then update the OS to 10.9.4. This should take care of any problems.
Although it involves spending a little bit more, another option is to puchase a dual drive kit and have both HDs on the laptop- simply replaces your optical drive slot.
The better option though would be to change over to an SSD- they are considerably cheaper than they used to be, but are far more reliable than a SATA. SATA failure rates can be quite high, and it is possible your HD that was involved in the liquid spill may have some bad blocks waiting to cause a problem. You should be able to track down a 2.5" 500-1TB SSD for $150 or less- depends on brand