I have experience with both (on an LP12), and much prefer the Linn . . . I think the manufacturing quality is better, and it's less fiddly to set up. The Grace's the anti-skating, with both fishing-line AND a pivot/weight thingey, mounted to a separate collar clamp that can move any which way sideways, up or down, (and affects the cueing as you adjust it) . . . really annoying.
But they're really apples and oranges as far as the sound, because they have their optimum performance with different types of cartridges. If you're using a high-compliance MM cartridge (i.e. Ortofon 2M or something) the Grace is a better choice, but for lower-compliance MMs and most MCs, the Linn will work better.