Trek what vs. Specialized what?
They both make low end and high end bikes. I'd be most concerned with how I liked the frame geometry.
Technically speaking disc breaks are not, and can not be physically stronger. But there are a lot of reasons to prefer them. (especially over super cheap V brakes)
Here is a picture of hydraulic v brakes. Probably the strongest break design for bicycle ever made. They however still feel like V brakes so people still probably given the choice would prefer disc.