I don't know about one being "stronger" than the other. I have a good deal of experience (several dozen trips) with both. From my experience, they are just very different trips. I suppose it is also worth noting that I have come closer to having a trip go awry with mushrooms than with LSD. There is something about the body effects of many mushshrooms I have taken that can really put me in an uncomfortable state. Also, I find LSD to be a much more "active" trip (for me). I feel much better motivated to go out and explore things than with mushrooms.
The last time I took mushrooms, I was with 4 other people, and we were in Washington, DC going through the museums. It is a thing that we loved to do on LSD, but mushrooms were the wrong substance for me. Every time my friends stopped walking for even 5 seconds, I would get down and lay on the floor. I just couldn't find the energy to keep going. Things became uncomfortable when a security guard at the Smithsonian started yelling at me for sprawling out on a bench. No one else who had eaten the same mushrooms had a similar effect.
So, really, I wouldn't call either one more "powerful". They just have very different effects for each person, and you must learn and respect that. You will eventually figure out which one better suits you, and know your affinities.
Oh, but as with any potent entheogen, respect your substance. You need to go into this with a responsible attitude and a clear mind. Know your companions and your surroundings well. By the time something goes wrong on your trip, it may already be too late.
S-Town