Aikido = modern martial art derived from ancient Japanese jujutsu, which was practiced by badass samurais.
BJJ = modern martial art derived from ancient Japanese jujutsu, wich was practiced by badass samurais.
Notice the similarity? Now here's the difference
Aikido = has a reputation for being practiced by blissed-out hippies who wouldn't know martial effectiveness if it kicked them in the bum.
BJJ = has a reputation for being practiced by macho meatheads who want to prove how tough they are and fight on TV in cages.
I think both of those stereotypes are deserved to a certain extent, but that both of them fail to paint a fair and complete picture of their respective martial arts. Still, to equate aikido with miyamoto musashi, and BJJ with meatheads is quite intellectually dishonest.
On the whole, I find the people at my BJJ club to be much more friendly, open, and less egotistical than the people at my aikido club: I find so many people to be very tense, arrogant, and unable to 'let go'; when I find somebody who displays this level of 'tenseness', and inability to 'let go' at BJJ, and I spar them, I am completely relaxed, and have no problem dominating them; in aikido, these people are never challenged - they continue, for years, with a level of tension in their bodies that I learned to let go of in my first judo ne waza randori.
To address the thread-starter: with aikido, you control the body, by controlling a limb (generally speaking); in BJJ, you control the body, then you control a limb (or the neck).
BJJ is a much safer way of pacifying a person than aikido, in my opinion; not only because it relies on skills that are easier to acquire, but because you are more likely to harm a non-compliant person by attacking the smaller joints (a large part of aikido is wristlocks), than the larger, stronger ones.
The context in which aikido, and judo, throws and pins, make sense, is one in which you have bladed weapons - so if somebody is vulnerable for a few seconds (after a throw, or during a pin), then they are effectively dead.
BJJ developed in an environment where this was not the case - confrontations were not frequently lethal - hence their focus on submissions - a focus that meant they could easily beat those martial arts who didn't train to finish a confrontation in such a way (a judoka trains for ippon - a 'KO' throw - but if there are no weapons involved, and the throw does not knock you out, you can continue to fight a judoka).