If price dosent matter, and you are willing to pay what ever it takes to get the best VR experience, I would say the Vive Pro, I normally recommend the Rift over the Vive, and would do 99% of the time.
But, if money isnt an issue and you want wireless VR than the Vive Pro is arguably the one to go for, not for the Vive Pro it’s self, but for the Wireless addon and the soon to be released knuckle controllers, one of the reasons I say to people buy a Rift over the Vive is because of the controllers, I hate the Vive Wands, the Oculus Touch controllers are better in every way, but, if money isn’t an issue HTC are releasing new Knuckle controllers, for the Vive and Vive Pro, which are more in line with the superior Oculus Touch controllers.
All this won’t come cheap, I believe you are looking at over £1000 for a Vive Pro with x2 lighthouse sensors, and x2 Vive Wands
£350 for the Vive Pro wireless adapter
And I’m not sure about the knuckles controllers, I would estimate around £150.
Wether that’s worth it to you is up to you.
I still prefer the Oculus Rift over the Vive, I love the user interface, and Oculus’s own funded games are amongst the best around, if you are planning on using a dedicated room for VR (I’m incredibly jealous of those people..) then there’s an overhead cable management solution called Midwec, that many people swear by, I would recommend looking into that rather than using a wireless adapter that ‘could’ cause frame loss and stutter.
Just to throw another option out to you, there is a company releasing two new headsets soon, the Pimax 5k and 8k, personally I wouldn’t touch them with a barge pole after my experience with an earlier VR headset, it was awful, and fell apart in my hands after 3 months, but that’s just my own opinion.