What the honors program actually gives you is more important than just the honors distinction, which is why I was asking. Getting an honors designation is nice, but it doesn’t really matter. If you have lots of other benefits, like easy access to research opportunities and mentors, good networking opportunities, priority registration, etc, then that can be beneficial to you, regardless of what the actual label is on your diploma/transcript.
But also keep in mind how feasible it would be to get those opportunities outside of the honors program. You can do research without being in the honors program, for instance. It’s really just weighing the pros and cons. I wouldn’t recommend putting any weight in the label of the honors degree, though. Instead, focus on the benefits that the honors program gives you–not the name.