I had watched the remake when I was in my preteen years, and didn't enjoy it as much as I had enjoyed rear window. As an adult I watched the original on TCM and was very surprised at how much I enjoyed it. I've recently rewatched the Doris Day version, and while I appreciate it much more than I did in my youth, the original is still a superior film in my mind. I really think the European setting is better than the dessert and while I absolutely think Jimmy Stewart is a talent beyond reproach, I buy the relationship between the family members more in the originally.
Things I noticed that had the Hitchcock style: the unique camera angles - the view of the stage from backstage, but not the typical side view of the performers, just slightly behind them with a small piece of the audience visible. The panning shot of the row of the audience- feels very familiar, but can't quite put my finger on specific scenes from his films The young lady emptying out her purse-that desperate search is very Hitchcock-ian to me, but again, can't currently name a scene or film example