This is a common question here, and it seems there's just really no correct answer. It depends on what you're most looking for out of the game.
Since positive and negative is so subjective, I won't list the following as pros or cons. Hopefully the list of general aspects will let you decide for yourselves.
Prophecies (Chapter 1, Tyria, just called "Guild Wars" on the box)
- starting the story in the beginning
- most free skills from quests
- largest content
- generally agreed to be a compelling story (again, opinions vary on what's a good story and what isn't)
- so far, the most likely chapter to be included in *most* special events, like Halloween and Wintersday.
- fewer players
in some areas (various reasons for this)
- It takes longer to get characters to max levels and elite skills than the other chapters
- possibly more confusing to follow given how much more rigid the requirements for following the primary quest lines in the later chapters got.
Don't get me wrong, it's not like the game doesn't tell you where to go, just that it doesn't force you the way the later chapters do.
- The AI teammates ("henchmen") are probably the most frustrating of the three chapters.
- The end-game, elite PvE areas are accessible to everyone. As they've been around the longest, it can be hard to find a group of random players that just want to explore rather than groups of random players on well-known, well-practiced, optimized "farming" runs. (IMO, such groups make it *a lot* harder to get in there just to check things out.)
Factions (Chapter 2, Cantha, says "Guild Wars Factions" on the box.)
- maybe better for people that like to PvP more than PvE, as Factions has the most interaction between PvP-play and PvE-play. Though the Factions-only PvP is a much different style of play than the campaign-independent PvP.
- Factions has the most PvE content that's affected by PvP results.
- the fastest progression of PvE characters to max levels, elite skills, etc. in PvE
- probably the fewest people playing right now
- This one is, again, just opinions, but it seems like of all three Factions is the one most people liked the least. Some people do love it, though.
- Some AI teammates (henchmen) are less frustrating than Prophecies' henchmen, but the really nice ones aren't always available.
- least accessible end-game elite PvE areas.
Nightfall (Chapter 3, Elona, says "Guild Wars Nightfall" on the box.)
- heroes. These are the new-generation henchman. You get heroes that you have a lot more customization and control over than henchmen. (you can take your heroes to the other chapters if you have both Nightfall and an another chapter on your account.)
- probably the most people playing right now, as it's the newest
- While they are all playable stand-alone, starting here is like starting a series of books on the third installment.
- The latest approaches to acquisition of armor and weapons in Nightfall is the most flexible to date, i think. With flexibility comes more ways to confuse new (and some old) players, though.
- The newest, and generally considered (for now) the hardest and least rewarding endgame elite PvE areas. It's more accessible to everyone, though.
- Generally thought of as a good story, better than Factions. I haven't seen enough response to feel comfortable saying if this chapter's story is generally considered better or worse than Prophecies.
- It takes longer to build "max" characters in Nightfall than Prophecies. It takes less time to build "max" characters in Factions than in Nightfall. It's impossible to say what you'll like best as a new player, but the general consensus seems to be that Nightfall has struck a nice balance between the first two chapters when it comes to character progression.
- Besides the heroes, the available AI henchmen are static and almost always available at every outpost. I haven't given them much testing thanks to my trusty heroes, but it seems like they're not as good as the really great ones from Factions and not as awful as the really awful ones from the first two chapters.
To those looking to play PvE with other people, note that a lot of people have multiple chapters linked on the same account, so just because you see more players in a town doesn't mean they're necessarily more interested in playing with other people. I've seen a lot of folks that really like to play with pick up groups in PvE complaining that the addition of customizable heroes has made it harder to find people to play with in all three chapters.
EDIT: Oh, and if you don't like abbreviations and acronyms ... this isn't the game for you!
That's all I can think of. GL to you guys finding one you like! I hope I've helped, and welcome to GW!

Luny