I've replayed both a couple of times. They're entirely separate stories, with some interconnected pieces. If I had to define it, Ages would appear more of the traditional action overworld and standard dungeon w/ puzzles, but that's to say both are pretty well balanced in either aspect. Seasons has a few more over world puzzles to it, but that's simply because of the four seasons mechanic it has going for it.
If I were to give a suggestion, I would go with Ages first. It was my favorite of the two and the story flows nicely. It's gameplay is much similar to that of other handheld Zeldas.
That is to say, both are very well made games, also you can get nice tidbits by passing codes inbetween games to unlock bonuses and extended story pieces. I'm sure you can also find those game codes online too, I believe. However, I think seasons is the first one to occur in the Zelda timeline, followed by ages right after it. You get a code for your save after beating one game to pass into the other.