Cant' go wrong with either IMO. I own the JC-1s and absolutely love them.
I've listened to the X350.5 at my dealers showroom countless times and could easily live with it.
The JC-1s just seem a bit better however in high-bias mode, especially in the midrange.
The Pass is MUCH better to look at however and I wouldn't be a bit surprised if you chose the Pass on looks alone. It's simply gorgeous.
They will both drive anything you want to connect to them. I run my JC-1's on dedicated 20A circuit for each amp. They will also both make your room very warm depending on climate.