Fossy is correct...
You basically have the original Global Express aka the "Classic".
Then they upgraded the Global/Classic with the XRS version which brought in some system changes/modifications and a higher pressurization differential. (BTW, the Global 5000 incorporates the XRS's upgrades)
Then when they brought in the Collins Fusion cockpit, they decided to name it the 6000. So the 6000 is the latest version of the Global Express which is in production.
I have not flown the 6000 because you need a differential course but I'm pretty sure all models fly the same way physically. Electronically the Fusion cockpit is light years ahead of the Honeywell based cockpit found in the Classic and XRS versions.
Because it is so different and more advanced I'm sure it incorporates things and systems that were simply not available or able to be included in the Honeywell cockpit. I believe in the Fusion cockpit you can have a weight and balance page available to you. The synthetic vision is awesome, the huge screens can display a multitude of pages and can even be split in two.
However, the Honeywell based cockpit with its synoptic pages covers most if not all of the aircraft's systems, so it's not bad at all.
I had the chance to sit in the Fusion sim here in Montreal and I tell you it is simply amazing. Wish we would have waited a few more serial numbers and gotten one... Oh well, maybe in a near future or maybe they are waiting for the 8000! :-)