Although I had a Linn Karik III for 4 years and have had a Wadia 301 for the last 9 months, I don't pretend to offer a definative comparison.
I have to concede to HiFinut604's point in that the Wadia is clearly a collection from other manufacturer's parts bins (and some fairly budget bins at that). While I'm sure Linn share similarities with other manufacturer's they clearly include much of their own design.
The transport/drawer unit of the Linn IMO is far better engineered than the Pioneer unit in the Wadia.
As for the sound, I had wondered if I'd made the right choice when I first used the Wadia. However, when I tried the Linn 8 months later when I was getting ready to sell it, I was surprised at how much better the Wadia was. It was also apparent the transport on the Linn was far slicker and more robust than the Pioneer unit.
A month after selling the Linn, I am now without a player as the Transport mech. has developed a fault (did I mention it was a pioneer?)and has been returned to the importer. This incident has undermined my confidence in Wadia especially as they only offer a 12 month warranty on the mechanicals and electronics (what's left?). When asked how long the repair would take, the dealer said he had no idea as he had never had to return one before.....A bit of a double edged sword!