Bitcoin ABC developers are real jackasses by using the exact same path for the data folder as the Bitcoin Core client. Not sure about how Bitcoin Unlimited works.
In any case.. I would use a different computer because I would be paranoid to install that software on the same OS that I have installed Bitcoin Core, at least a different partition.
You can use the existing block files of the Core folder into the ABC/Unlimited folder to speed up the process (copy all blocks until August 1 2017), so they are only validated and not downloaded (download starts at August 1 2017+ blocks). It's still pretty slow to validate years of blocks tho, may take a couple of days depending on the computer.
Chainstate folder cannot be reused.