So I understand it is not the Windows itself that you want.
In that case you can use any external/removable medium big enough and preferably an HDD. Flash disks/USB sticks act weird sometimes with large files.
Such files like movies and music can just be copied directly without any special tools. Just locate them on the source computer and copy them to the external medium.
Some stuff however are better moved with special tools made for them, like browser history, tools, setting, plugins, etc. Those can be archived into single files then restored into another computer with the supported browser. Firefox for example uses Mozilla Backup.
Also software, including games', settings and progress could use the user's folders to stores stuff like saved games. The user folder (a folder called "Users" in the OS's root) should be copied to preserve those if they are important.
I hope that helps. But yes, if there is a software that can do all the above in simple steps, it should be okay. If Easeuse does that, then your problem is the USB stick. It's probably not formatted right or something. Some software refuse to use USB sticks and require actual HDD's or composite disks (CD's, DVD, etc.).