Cid is more mental and Shrooms are more emotional. You can do more activities on cid but shrooms will make you want to stay put and observe. Both are much better in nature.
Saw this video the other day where a dude records his first mushroom trip and first acid trip. The mushroom trip takes place in a native american tipi, with a native american shamen type dude. The trip is spent the whole time sitting there just experiencing the trip. The acid trip takes place indoors in a brightly colored apartment. The apartment has tv and video games, with brightly colored shaggy carpets, and 70s style pink and green patterns running up and down the wall. The trip is spent playing video games, crawling on the floor, sitting on the couch, looking in the mirror, roaming the kitchen. Both these seem to be perfect locations and resonate really well with their corresponding trip. Mushrooms have a tendency to ancient feeling, straight to the point, spiritual, alien. Acid on the other hand is much longer and comes on in waves. This gives more room for exploration. Its bright, energetic, playful, extremely visionary.
In my experience, lsd is easier to control than mushrooms. At high doses, either one is going to kind of put you in its back pocket and take you where it will. You just need to relax and let go and learn. Mushrooms to me seems older and wiser and much more dreamy and earthy. It is easier to get confused and somewhat lost on mushrooms than with lsd in my opinion. However, I find it difficult to compare the two since they are both definitely unique and yet at the same time similar.