Just a small note, Elder Scrolls is a series, which Skyrim is a part of.
Anyway, we can at least confirm that each shrine is built around a gimmick, that being whatever enhancement or ability you receive in each shrine, so they'll have that going for them. From the few we've seen though, they don't seem like much more than demonstrations of your new ability. With some hidden goodies in chests. I suppose again we'll have to see how it goes when the game comes out, but, at least for that aspect of the game, color me cautious. I'm incredibly hyped for the overworld gameplay, don't get me wrong, but fun and solid dungeon/labyrinth/shrine gameplay to complement it would be nice, ya know?
Also now that Psynergist mentions it... Yeah. My experience with Oblivion (my only Elder Scrolls game apart from a bit of Skyrim before realizing my PC won't run it well) is that you're in it for the towns and quests and storyline more than you are dungeon-crawling. All the caverns and ruin systems are incredibly samey, and honestly aren't very fun to navigate. Most of the puzzles within don't have much variance, and it's uninteresting to be honest. There's a lot more fun to be had walking around the overworld and discovering new places, which is definitely what I expected to be having the most fun with in Breath of the Wild. The shrines at the least seem at least far more varied and unique than any of Oblivion's "dungeons," but for the most part... yeah, the comparison seems apt.
It'll just probably be a little more fun to play because I much prefer Zelda's play style and controls over Elder Scrolls. 