MacBook Pro can’t mount an exFAT external hard drive when having too many files

This seems like an issue with the chosen file system.

What file system did you choose when formatting the hard drive? If it's not HFS(+), FAT in any fashion or NTFS you cannot read it on OS X without additional software. If it's Ext, you could go with Paragon's Ext for Mac (but it costs some bucks).

In future, best choose exFAT when formatting an external hard drive if you need to use it on different operating systems. It both allows rather large files (which is heavily limited in FAT32), but can be both read and written in all important operating systems.

I'm assuming you have nothing on the new disk and essentially want to mirror what is on the old disk to the new disk.

You can use the following command line, substituting the proper names for Source-Disk (old) and Destination-Disk (new).

rsync -xavH /Volumes/Source-Disk/ /Volumes/Destination-Disk/

Note: The slash at the end of each path has significance, so don't forget to include it when changing the name of Source-Disk (old) and Destination-Disk (new). Also, if there are spaces in them, make sure you either escape the spaces with a backslash \ or quote the pathnames, but not both.

Explanation of the options used:

-x, --one-file-system    don't cross filesystem boundaries
-a, --archive    archive mode; same as -rlptgoD (no -H)

    -r, --recursive    recurse into directories
    -l, --links    copy symlinks as symlinks
    -p, --perms    preserve permissions
    -t, --times    preserve times
    -g, --group    preserve group
    -o, --owner    preserve owner (super-user only)
    -D    same as --devices --specials
        --devices    preserve device files (super-user only)
        --specials    preserve special files

-v, --verbose    increase verbosity
-H, --hard-links    preserve hard links

Note: Because symlinks are being copied to the Destination-Disk volume the volume name of the Destination-Disk will need to be renamed identical to the Source-Disk, afterwards, for the links to files on the disk itself to track. See the SYMBOLIC LINKS section in the rsync man page for additional options that can be used to modify how the symlinks can be treated.