As long as it doesn't exceed 50,000 files, it should be okay (I however suggest to keep as far away from the limit as possible due to how it can break things).
FTP would be a simple way to just download everything from your old server onto your desktop. Then login here via FTP and upload everything from your desktop.
with some CMS accounts (i.e. like WordPress) there can be a issue with the size of the Zip file - x10hosting's users do not have much room (i.e. amount of ram) to up-load and extract files from a large zip file and it can be more than 512 MB in size which is the limit of new x10hosting's free-hosting accounts