What are the advantages and disadvantages of becoming a vampire?

Unfortunately (or fortunately), you don't sparkle, and Anna Paquin isn't instantly attracted to you. There are other perks and drawbacks that might offset that, though:

Benefits

• Immunity to disease, and any disease you contracted will be cured
• Immunity to poison, and any poison you contracted will be removed
• 25% boost to Illusion spells cast
• 25% harder to detect while sneaking
• 25% boost to frost resistance per stage of vampirism (to a max of 100% at stage 4)
• Special, vampire-only powers (see below)

Drawbacks

• Your face transforms into something only a mother could love; NPCs will comment about it, too
• NPCs will attack you on sight once you hit stage 4
• No magicka, stamina, or health regeneration during the day
• 15 point reduction to magicka, stamina, and health during the day per stage of vampirism (to a max of 60 at stage 4)
• Weakness to fire increases by 25% per stage of vampirism (to a max of 100% at stage 4)
• Cannot become a werewolf, and lycanthropy will cure vampirism
• Must feed periodically to maintain lower-levels of vampirism, which is a real hassle and is considered a crime

Vampire powers

As mentioned above, vampires get a set of powers and abilities in addition to their bonuses:

Stage 1:

• Vampire's sight — 60 second night vision; no cost, no cooldown
• Vampiric drain — drain life, 2 health per second
• Vampire's servant — Reanimate level 6 or lower corpse; 1 day cooldown

Stage 2:

• Vampire's seduction — mob level 8 or lower won't fight or flee for 30 seconds
• Vampire's servant now works on level 13 or lower corpses

Stage 3:

• Vampiric drain now drains 4 health per second
• Vampire's servant now works on level 21 or lower corpses

Stage 4:

• Embrace of the shadows — Invisibility and night vision for 3 minutes; 1 day cooldown
• Vampiric drain now drains 5 health per second
• Vampire's servant now works on level 30 or lower corpses

Even though this was answered a long time ago, I'm going to give a slightly different take on the answer with some additional information from a short time playing as both. I won't go into the perks of both since that has already been done.

NB: This answer relates to Dawnguard although the original question pre-dates the Dawnguard expansion. However, since many people, like myself, may think the original question is about DG, I will leave this answer here with the permission of the moderators.

• Quest differences and location:

From the point of view of quests, if you compare the quests for both factions you'll see that the locations don't have much difference to them. The first quest for each faction is different, but after that they're largely the same apart from the fact that you're either playing Dawnguard vs Vampire or vice versa. The current Wikipedia Dawnguard article mentions this, saying:

if the player character refuses Harkon's offer [of becoming a vampire] and returns to the Dawnguard, the plot plays out nearly identically, albeit viewed from the perspective of the Dawnguard.

Obviously, you will not have access to Castle Volkihar if you choose Dawnguard or Fort Dawnguard if you choose the vampire side. Functionality-wise, the Fort is much more focused on weaponry and has a blacksmith, general goods merchant, arcane enchanter and forge. The Castle is more magic-orientated and has access to the Bloodstone Chalice, Amulets of Night Power, and Rings of Blood Magic. Looks-wise they both have a Gothic feel to them, though the Fort is more classical-Gothic and the Castle is more horror-Gothic: their locations match this since the Fort is in the auburn leafy clearing of Dayspring Canyon near Riften, whereas the Castle is the inhospitable cold of the sea west of Solitude.

• Daylight exposure and travelling

As a vampire you do have to be careful when out in the sun. I play as a Redguard and like to explore Skyrim at all times of the day and night, and being out in the sun can damage your health [this does not apply to houses/caves/dungeons though]. If you like to fast travel this can cause problems, with sun damage or death being the result. Additionally you can get attacked even by your own brethren if they discover you're a vampire pre level 4 - I was killed by my own housecarl after he discovered. If you're level 4 you will get attacked by NPCs, pretty much everyone hates you.

• Physical appearance

Something else which hasn't been mentioned is any alterations you want to make to your character appearance. I'm the kind of person who likes to make occasional small changes to my character's appearance [hair/warpaint] via Galathil in Riften. When you become a vampire you get glowing red eyes all the time, and I felt that these didn't go well with my look, so I wanted to make changes to my character's physical appearance to match them. However, if you go to Galathil after becoming a vampire she will say she cannot make changes on the undead. Even the 'showracemenu' console hack will not work. Additionally, your appearance will become more haggard the longer you don't feed. If you're the kind of person who cares about your character's look, these things can bug the hell out of you.

• Your character ethics

It also comes down to whether you want to play weapon-based as part of a faction for the better of Skyrim, or magic-based for the betterment of your own personal cause, and how well these tie in with the kind of character you're playing [though you can mix and match, of course] and what they would do.

Choosing Dawnguard is not the end of your potential as a vampire. You get the opportunity to become a vampire again in the Chasing Echoes quest, you can also switch between vampirism/lycanthropy if you ask Aela when the questline is over. You can still become a vampire Lord after completing the main questline by asking Serana to turn you, as long as you have not cured her of vampirism first. Either way, you will still get endless radiant quests for either side.