I've had both as well, and really enjoyed both. They didn't work best with the same speakers. The Classik worked really well with Silverline SR 12's but the L40 didn't. The L40 makes an old pair of DCM Time Pieces sound great, and worked well with B&W DM302's.
And a guilty admission - I use the L40's loudness button when I listen at low levels, it offers more of a difference than the Classik's tone controls do.
You get the AM tuner with the Linn, but you have to get special speaker cable connectors.
There's a learning curve with either remote, but the Classik has the better one, and it is also nicer looking, and it is also more than twice the price new or used.
Neither one will enter you in the competition for extracting the last 5% of musicality from the source, but I don't think that compulsion drives the purchase of an all in one unit.
If you have speakers, try to audition a player before you buy, if not pick your price point and get ready to enjoy.