Hi PrimozK,
I am no expert on the running of X-plane 10.
Before you purchase the software check the specifications of your two units, This can be found on the main X-Plane website. If all OK then download the demo version to your laptop and your PC to see if it will run. The demo version has a short run life and operates from one airport in the States.
One issue that needs to be considered for the laptop is that it has adequate cooling especially for the processor. If not the system will crash. It is much easier to add additional cooling to the PC.
Once you have acquired X-plane in a 10 disc boxed version, rather than digital version download, consider purchasing the USB key rather having to insert Disc 1, as suggested by Rishi, every time you want to run x-plane.. This unit woks just fine (I have one) and this eliminates any future risk of your disc being damaged. The USB unit can be obtained from the following link http://www.x-plane.com/store/desktop/x-plane_10_home-use_usb_key/. This allows you to travel with X-plane on your laptop and the discs can be left at home in a safe and secure site.
The same referenced site also makes mention about security for a digital download,
Hope this is of some help.
Happy flying.
Glenn