I'm an old hippie who has a lot of experience with said drugs in this thread. I'll give you my opinion...I don't claim it to be fact..."It's just, like, my opinion man." (points for a Big Labowski reference?)
In short, they are nothing alike.
But....that doesn't mean they don't get along well together or have some innate similarities. In my mind being alike and having similarities are not the same thing (i.e. you wouldn't use either for a substitute for either). I thoroughly enjoy them both separately and sometimes together.
They are both great fun at concerts. Although, I wouldn't recommend tripping at a concert unless you have a few good, hard, weird tripping experiences under your belt.
MDMA is a guaranteed good time. LSD is that way for me, but not everyone. I have eaten from a half hit all the way up to a ten strip and never had a "freak out." But I have seen many people have horrible freak outs and it ain't pretty. I've even babysat my fair share of freaked out kidz with headfulls of acid. No one who has family history of mental issues should really do LSD.
LSD is definitely more for your thinking person, MDMA is just pure fun. LSD can turn on you and make you frighteningly introverted. You have to be comfortable with what you might find. Some of my favorite trips was where I spent hours by myself just thinking.
If you are looking for a more intimate time with your guy or gal for a night of sex the great news is they both are good for that. HOWEVER, LSD is in my opinion better to fuck all night on for the guys because you can actually maintain an erection and finish. Both of those get next to impossible when you're rollin'. It also should be said that it likely won't matter in the least to you or your partner if you can't finish or stay hard all night while rollin' because you will most likely be feelin' too good to care.
LSD will likely get weird on you at some point...but that's sort of the fun of it. Bottom line....LSD is not for everyone, do research, know what you are doing, know your source, and spend your first few trips somewhere with very trusted and experienced people in a controlled environment.
D.A.R.E to think for yourself.