Just been wondering this exact thing.
I do like using my modern full-suspension as its fun to ride and this being the case, then yes it makes me better as I want to go out and I am willing to be more adventurous on it. Suspension and disc brakes are great, but my Shimano gears are too smooth for a MTB. Basically its a blast!
That said, if I ride it more than my other bikes, it makes me lazy and a sloppy rider. My rigid bike forces me to think about what i'm doing and can be unforgiving if my mind wanders. I get a lot of satisfaction and fun from a rigid bike.
Very basically, they both make me better by pushing me in different areas. I timed myself on a regular run the other day and my rigid bike came out quicker (3min over 10 miles).
Either they both make me better or make no difference at all, but I like having old and new and tend to split the time quite equally.