Without seeing your essays, it's tough to say. In general it's definitely much better to be positive than negative. However some things are just plain bad and would deserve a little negativity. You don't have to be a Pollyanna, but don't put down others or play the blame game. And if you are dealing with something bad, focus on what you did to improve the situation and what you learned from it -- not what someone else did to create it or make it worse.
I guess I'm still saying focus on the positive.
Also, remember that the essays are supposed to be mostly about you. You definitely don't want to be negative about you.