I was reading through some essays online and they seemed to be primarily geared toward a single, defining topic, but my teacher suggested that I try and put as much of myself in the essays as possible. This made is difficult to choose whether to write about a single event in depth, or to try and capture as much of my life as possible
Which way is better? Would colleges be able to just look at the application, making my teacher’s advice useless?
No single way will be inherently “better,” as is usually the case with most writing. It’s all about execution. I’ve always heard you’re supposed to do a combination of both: tell a single, defining event that then illuminates the rest of your character–all in about a page.
Just try a few different essays and submit whichever one you like best! I’ve written my essays a couple times over and over to see what feels best. 
The general advice is that it’s better to write about a single – meaningful – event in depth.
I think what your teach meant by that is not to debate pro-or-con for an issue, but let the issue topic be a vehicle to reveal something about u.
Do NOT try to “capture as much of my life as possible”. The essay is not a CV. It should not be a rehash of your career choice, your achievement awards, and your summer internship working in a lab.
Pick an event, an issue, a theme. Then describe how you impacted it or it impacted you. It is not necessary (or even possible) to reveal every angle of your character. Focus on the depth of essay topic, not the breadth .