to the Original poster, memory and storage are two different things. Memory refers to RAM while storage space refers to the Hard Disk Drive.
I am assuming since you post is labeled "Hard Drives" that's your asking how hard will it be to replace the hard drive in the new machine with the one from you old one.
First you would have to compare the motherboards, if they feature a similiar chipset (note this does NOT mean processor/cpu) then there shouldn't be much of a problem.
I would recommend that you simply add the hard drive to the new machine.