I actually own both jackets and I love both in different ways. The precip postitives are: lighter, packs down smaller, fits better and has never let me down in the rain. Precip negatives: more crinkle sound with movement and I do not like the separate hood and collar(really hate this part). The minimalist positives: less crinkle, material feels tougher, better sealing zippers. Negatives: doesnt pack quite as small, the torso is a little short so my base layer does slightly stick out on bottom, annoying but not a deal breaker. Hope that helps some. Can't go wrong with either but the precip is half the price. Something to consider along with your intended purpose.
For reference I am 6'1", 195lbs, in shape and I have both in large