Most people compare the three, because they are all hack and slashes. Zelda is an Action-Adventure. I do somewhat agree with your comparison though. God of War does have alot of puzzles, and Dungeon Crawling like Zelda, but there are many differences. The first one is mini games/Side Quests. Zelda has many of these especially in Majora's Mask. God of War doesn't have any of these, but that is ok since they are two different genres.
Another difference is that zelda uses more items in the puzzles, while god of war is more of pushing and pulling things.
Then you have the very different combat systems, which is relative to their genres.
Those are just some of the obvious ones that you haven't mentioned, but there are many more. I don't think Action games should be compared with Action-Adventures. God of war takes many different aspects from many different games, and puts it in one, so I think it compares to both. I forgot to mention that TP isn't a good representation of zelda games. Especially the 2d ones. The 2d zelda games were far less sectioned, and less linear. Its hard to compare anything to zelda, because almost every zelda game is different.
Off-Topic How are you enjoying TP? More than you were a few weeks ago? Where are you at? When you finish, and if you are interested in playing other games in the series I recommend Alttp(Excellent Gamplay, and made most of what zelda is like today, and Majora's Mask( A more charcter focused game, so if you like those then it may be your favorite. It is very depressing, and has a very good central theme)







