First thing you will need to confirm is that both servers are running the same subversion server, you can determine this on either Linux or windows by getting to the command prompt and executing 

svnadmin --version

this will return what version you are running.

Windows

Linux

If you look close I am not even at the exact version but this worked for me.

Now you will need to export exact repository, if you google it there are allot of examples and allot of options, you can just export the last 10 versions for example. In this example we will dump the entire thing to one file.

svnadmin dump /path/to/repository > repo_name.svn_dump

or windows

svnadmin dump C:\path\to\repo > C:\repo_name.svn_dump

C:\ is just for example it can be any drive or share path

This will take a little time to export and each version is exported separately, if you run it in silent mode you will only be notified when it is complete, depending on its size it will take a little time.

Once you have your *.svn_dump file you can move it to the new server.

To import this file and make the same repository you must use the svnadmin tool.

svnadmin create /path/to/repo

svnadmin load /path/to/repo < /path/to/repo/dump/repo_name.svn_dump

to maitain the uuid's ad this tag like this.

svnadmin load --force-uuid /path/to/repo < /path/to/repo/dump/repo_name.svn_dump

Again windows paths are the same syntax with the slashes the other direction like above in the dump example.

Links I found info on,

http://www.petefreitag.com/item/665.cfm

http://www.digitalmediaminute.com/article/2251/how-to-move-a-subversion-repository

http://www.newlc.com/en/migrating-subversion-database-version-14-15