Original strings

If you like the EBs on your Shector, then I do not see why you shouldn't try them out on your Squire.
The Squire either came with Squire or Fender strings (musiciansfriend.com carries both brands).

 

Try the EBs, try the DRs, try everything and see what you like. Who knows how long those strings have been on the Squier? No matter what they are, they're probably half-dead. . .

 

On your Schecter, you are noticing/liking (I think) the newness of the strings and not that the strings are Fender strings versus Ernie Balls. While each string brand may have a slightly different sound to some people's ears, the difference between new and old strings can be striking.

Most instruments I've played in any price range automatically come with decent strings, including Squiers and all the rest. They just may be dead (if you bought from a store and it was on display).

Hope this helps.