The two, most-important differences between these two models is that the Pelikan has a dedicated piston-filler, and the pen's diameter is considerably wider than that of the CP1. The Lamy CP1 is a cartridge/converter pen and its diameter is close to that of a standard, round wooden pencil.
Bottled ink converters can, at times, be a problem because of poor manufacturing tolerances of the converters. I have never had a problem with the Pelikan piston-filler, including taking M600 pens in jet aircraft (no leaks).
The M600 is serviceable: the nib unit can be removed/changed; the ink reservoir can be easily cleaned and lubricated.
The 14K gold nib of the CP1pt can be easily changed. Lamy proprietary cartridges in several colors are available and Monteverde also manufactures Lamy-style cartridges.
Although I have used, collected, and enjoyed using Lamy writing instruments for decades, I would choose the Pelikan M600 model over the Lamy CP1.
However, I must say, a fairer comparison would be between the standard Lamy 2000 and the Pelikan M600. Although the M600, with its various color choices, may be considered, by some, to be a prettier pen, just considering price, the L2K may be the better choice. The Lamy 2000 fountain pen can be dismantled and re-assembled without tools for cleaning and service, and it is an elegant, Bauhaus-inspired design. Like the M600, I have never had a problem with the piston unit of the L2K.
Ought to be pinned for future reference, a spot on comparison.