Soccer players get significant head trauma, the brain damage is almost as severe as football players. The one good thing about soccer is they don't make you bulk up.
True; but, the big difference between the two sports is that violent collisions in football occur just about every play where as it soccer, it is not a core part of the sport. In soccer, you don't see two players running full speed, lowering their heads, and ramming into each other just about every play because 1) its a foul, and 2) the player with the ball would be dispossessed just about every play. Generally, soccer players try to avoid running into each other.
In soccer, concussions occur from three primary sources.
1) The first and worst impact injury is when two or more players all go up for the same head ball resulting in head to head, head to arm/elbow (sometimes done intentionally), and then the subsequent fall. The rules have cut back on the violence as going over the back, pushing, and flying arms are now called as fouls and sometimes cards. Not sure what else can be done without eliminating that type of play, which would change the sports; but, not kill it like eliminating tackling would do to football.
2) Second is heading in general, which gets a lot of press; but, is, in my opinion over blown, at least for adults. Proper technique in terms of how and where to hit the ball with one's head shoudl not result in a concussion. I have played soccer for 30+ years and have not receive a single concussion from heading a ball. Broken nose, yes; but, that is a result of poor technique. Concussion from an elbow, yes; but, that is a foul. That said, there is some evidence that kids should not be heading the ball until they reached adulthood due to the incomplete physical development. The same could be said of tackling in football in general.
3) Third is accidental or indirect such as hitting one's head on the turf hard after a tackle or taking an unexpected shot to a bad spot in the head (my last two concussions in soccer were from this - taking a hard shot to my temple from a soccer ball that I was not expecting and did not have time to either avoid or turn my head into it to use my forehead). Allowing protective equipment can help (see Petr Cech) reduce potential injury; but, this happens in every sport - baseball, hockey, even tennis.