In short, the answer is both, neither, and "it depends."
Yes, really helpful I know, but allow me to expound what I mean.
Many expansions to games are meant to enhance the game, to give it greater variety, basically to get players to come back to the same game. Unfortunately, what often happens is that an expansion so drastically alters the game, that it requires players to essentially learn an entirely new game. Now, that's not a horrible thing, but if it takes a fast game and makes it extremely long, then there's a problem.
I think that the best thing I can do is talk about specific expansions.
Let me start with Pandemic: On the Brink. In Pandemic, there are 5 roles for the players. With OtB, I believe the total is up to 12-14, I'm not sure but it's a lot more. This gives players great variety, and most importantly, doesn't change the way the game is played. Now, OtB also comes with modular expansions, which can be used or not at the discretion of the players. This gives experienced players something new to explore, while still keeping the game friendly to new players. This is the best expansion to a game I own.
Another example is Settlers of Catan. The base game was fairly simple, but offers some choice, and a short playtime. The Seafarers expansion added exploration, boats, and scenarios to the game. This gave some variety, but also added to play time. I like Seafarers, I don't think that it's a required expansion, but it does give some extra options. The big change to Catan is Cities and Knights. This is basically the new game. There's a lot more depth to choices, and a lot more that players have to balance. Because of this, the game does take longer. You're looking at a 2-4 hour game depending on player count, and at times, that's just too much for Catan.
I'd be remiss to not mention Cosmic Encounter here. There have been 3 expansions so far, with more planned. These expansions have added 20 new powers, which drastically increases the permutations of different games you can play. Each expansion also added 1 new thing you can play with, Rewards cards, Hazards, large group cards. The players have choice with what to put in or not, and those are great.
Those 3 games fall into the Content Enhancer category. Catan maybe the least so, it really depends on your bent.
2 big games fall into the category of Milking the Cash Cow. I think they both started as content enhancers, but now they border on absurdum. Those games are,
Dominion and Carcassonne.
I love Dominion, and I think Carcassonne is a lot of fun, but when is enough enough? Does anyone really need 600 unique Carcassonne tiles? Does anyone need 250 different Dominion cards? Well, the answer is if you play it enough, sure. I mostly play Dominion online these days, and on there, the card variety is great. In real life, it's a pain to store, to set-up, to randomize, and thus it doesn't get played much. I was happy with 2, maybe 3 expansions. That gave me around 100 cards to play with, which is a lot of variety. As for Carcassonne, the base game was not enough. But I think the only necessary expansion is Inns and Cathedrals, and depending on the day I might argue that the River is necessary. Beyond that, I like Traders and Builders for variety, throw in the River 2, and I'm satisfied with Carcassonne.
Overall, I think some expansions are good. I like playing new games but I also like playing the same old favorites. Sometimes the favorites get dull, but a new expansion can breathe new life into the game. I think what I want to see in an expansion is something that changes the game slightly, like say a new map in Ticket to Ride, or new races and powers in Small World, while preserving the basic mechanics of the game. Expansions can add a bit of complexity, since you are targeting people who already know the game, but an expansion should not fundamentally alter the game. Give me variety, make the game experience better, but don't double the playtime, or even add more than about 30 minutes to the game. It's just too hard to keep people interested.