Both Pete and Walter are still bowling. I am not so sure that Pete would not take Walter now. Also, did Walter compete in the Open? If so, I would say that Pete beat him, just not head to head. Pete could compete with and beat any of the best on a good day.
To determine the greatest of all time you have to set the criteria you are using. Most money won. Most majors. Most top three finishes. Best physical game. Maybe a combination of factors weighted on a sliding scale. Otherwise it all comes down to subjective opinions about what matters most.
Those that can do. Those that can't complain. Pimpin ain't easy, but it's mandatory.
Most things we like, we don't need. Most things we need, we don't like. Don't confuse your likes with your needs.