For a job interview, should you dress in your most professional clothes or try to match the culture of the company you're interviewing with?

This is to settle a debate with my mom.

I am interviewing for technical jobs. Some of the companies I’m looking at have “business casual” or above dress codes, but, for the most part, the engineers at the companies I’m looking at come to work in t-shirts and jeans. I’ve had one in-person interview so far. The person interviewing me was wearing a t-shirt and jeans. I showed up for the interview in a t-shirt and jeans.

Basically, my mom is encouraging me to buy a new suit, white shirt, tie, etc. to look professional. I insist that I should dress to match what people at the company wear.