Anybody have experience with 1.25" and 2" hitch racks?

My wife's current car has a 1.25" hitch, and we have a Yakima Hold Up 2 rack. But, after a little over 7 years, it's showing its age. So, we should probably consider getting her a new rack.

The new car we are getting her can do a 1.25" or 2" tow hitch. I'm wondering if a 2" hitch is measurable more secure for the rack or does it not matter much.