Each of the Mario Party games seems to have its own best points, as well as its own shortcomings. I'll see if I can nail down a few, in my view.
Mario Party 1:
+ It was the original, so it had the "newness" to it.
+ It was mean (the minigames offered no mercy.)
+ The ? spaces really did something.
+ It was unpredictable (those blocks that you could buy? Brilliant. You caould be one square from the star, and yet there's no assurance that you'd get it.)
+ Each board map had its own distinct feel.
+ Great music (by far the best "you've got a star!" tune.)
- The rotating minigames.
Mario Party 2:
+ Introduced the concept of dueling (hoo, yah! Pirate duel is the best ever!)
+ Introduced the concept of battle games.
+ Introduced the concept of items.
+ Had many solid board maps.
+ Yoshi makes a very cute pirate.
+ Bowser's Big Blast!
- Since items were new, there were many problems (a plunder chest could sour the entre game)
- The archeology level was lame.
Mario Party 3:
+ Item system was duly refined.
+ The 2-player duel mode was a nice touch.
- ? spaces were a joke: "something's gonna happen now! ...unless you don't want it to. Do you want it to?"
- Mini-games were nothing spectacular.
- Board maps were blah.
Mario Party 4:
+ The mini-games were superb! (Almost every one was really fun!)
+ The Bowser games were great (we actually cheered for Bowser!)
+ Being able to choose a battle game (Bowser's Bigger Blast... well, it's not QUITE the same.)
+ Volleyball!
+ Decent music.
- The item (mini/mega) system was a joke.
- The board maps were rather unremarkable.
- No duels (WHAT WERE YOU THINKING!?)
Mario Party 5:
+ By far THE BEST item system to date! (The capsules were just what the series needed!)
+ Duels are back (there are some great ones, and some awful ones.)
+ Being able to vote on the battle games.
- "Super Duel" mode is just tacked on.
- Too many "pure luck" games.
I'm sure there are a lot of things I've missed. I can't really decide on any one, though. But get 1's unpredictability with 4's mini-games and 5's item system... hoo, yah...