I understand your aversion to renting a car (and driving) in Germany. I've spent almost 160 nights in Germany since 2000 on 11 trips (that's 170 "tour" days), and I've never rented a car. In fact, after every recent trip, I've compared what I actually spent for transportation (mostly all regional passes, individual regional tickets, and a very few adv. purchase long distance train tickets) vs what it would have cost me for a rail pass or a car rental, and I've always find I saved a lot of money my way.
I guess I'm not your prototypical American traveler. I eschew big cities. I've spent most of my life in or near major metropolitan areas, and for me, a vacation has always been somewhere out of town - Yosemite, the California redwoods, Olympic Peninsula, Mesa Verde, etc. Eighty-five percent of my nights in Germany have been in towns smaller than 20,000 population. I've spent enough time in Germany to feel completely comfortable traveling there, and I speak enough German not to panic if nobody speaks English.
So, to answer your question, GaPa is not the same as Berchtesgaden, and IMO, it's nowhere near as desirable a destination. First, Kehlsteinhaus (The Eagles Nest) is totally unique. There is no feeling that can match standing in the octagonal room at the end and realizing that Hitler and other Nazis, and Mussolini, were once there in that very room where you are standing. And a cruise on Königssee is beautiful; be sure to go all the way up to Salat and walk over the bar to Obersee. It's beautiful (Beautiful, big and beautiful, I'm beginning to sound like Trump!)
In 2000, I stayed in Freilassing and commuted two days to Berchtesgaden. I thought that would be less expensive than staying in a resort area. No, Freilassing was more expensive due to it's proximity to Salzburg. Since then (three trips, eight days), I've always stayed in Berchtesgaden. In 2012, I spent a 2 nights in Berchtesgaden before starting on my trip on the Alpenstraße.
As for GaPa, in 1988 I made a day trip from Munich to GaPa. I went up the Zugspitze, but for someone from Colorado, it was not impressive. The top of the Zugspitze is lower than the parking lot at the ski area (Loveland) where I often skied at home. The top of Pike's Peak, at 14,410, where I've been, is more impressive.
I think you should do Berchtesgaden, and three nights would be a minimum. Four nights in GaPa, IMO, might be a little overkill. Going from GaPa to Berchtesgaden does usually mean going through Munich, but there is another route I think you should consider. It probably takes two days, but it's interesting. It's not as fast as going through Munich, but it is scenic, and interesting, and has some historic significance. @me.crewe alluded to it in his post about a route through Murnau, but this route goes through GaPa, not Murnau. It's called the Alpenstraße.
As I understand, Hitler actually "designed" the Alpenstraße as a road to show off the Alps (or maybe it was Lugwig I, but Hitler had something to do with it). It's entire route goes from Lindau, on Bodensee to Berchtesgaden. Over 17 years, I've actually traveled almost the entire route, either by bus on the road, or on the train route paralleling the road.