This is a HUGE matter of opinion. It works in other forms of media/entertainment, too. With movies, the 1st and 3rd are always considered the best while the 2nd movie is overlooked. And when it comes to trilogy books, the first always seems to be the fan favorite of the series. Still, all opinions.
Now I want to know if Parappa The Rapper 2 is better than 1. Heh.
yes it is opinion, but when reviews come out that is what happens most of the time
from what i can gather its this:
The first game establishes that these characters exist and their world and also figures out what gameplay mechanics work and which ones dont
The second game seems to perfect everything that the first game was. It also receives a ton of hype because the first game.
The third game receives even more hype than the second but, since most of the substantial new features were added in the second game, the third game has a hard time living up to the hype. That usually ends up hurting the third game
^This EXACTLY! Though sometimes the 3rd installment does get recognized as better, mostly the 2nd outshines because of the above reasons AND nastalgia. Nastalgia plays a nasty trick on ppl and makes them "remember"
things that just aren't completely true.
Take Zelda OOT for instance (though it's not the 2nd game, I'll still use it as an example). For many it'll be known as the best Zelda ever, but if you go back to playing that after playing WW, TP, or SS, the only thing that'll make you feel that OOT is better is good ol nastalgia. Sure OOT was an OMEGA huge jump in the Zelda series but outside of that it doesn't have too much on the newer installments. Actually the newer installments have certain drastic improvements, but it doesn't matter because nastalgia tells us OOT is the best hands down.
The same goes for just about any other game (UC2 and UC3, Sly 2 and Sly 3,KZ2 and KZ3, etc.) In a nutshell, once something is defined as "Perfect", "Classic", or a "Masterpiece" it's hard to top in the eyes of fans regardless of what one does.
The first game is just a grasp on the concept. The second is where everything is really well refined and the rest of the series is cemented. The third is where a bunch of crazy **bleep** is added.
I've only seen like four video game series NOT follow this rule.