There's three sides to any player, and one usually stands out as being the dominant trait... though they usually cross over into each other.
The hobbyist.
This person loves to paint, convert, theme, etc. This is the person who will take more time working on their army. What does VC offer? They offer endless conversion possibilities provided you have the devotion. Want to make undead Dwarfs? Go ahead. Vampires and the undead of Nippon? Bring it! A mishmash of undead from as many armies as you can converted? Cool! Straight undead? Can't beat a classic.
There are plenty of ways you can make your army "your own". Plenty of freedom to paint as you wish. Demons do offer some, and Dark Elves are more limited. Not to say they don't have the freedom here, they just don't have the same degree.
The roleplayer
This is someone who gets into the background, sometimes called fluff, of an army. Be it the base background offered by the book, taking the background and building upon in, or creating their own little story in the Warhammer world. This is what the roleplayers are.
The VC have a very well established background, but offer enough variety to create your own little story. Be it an Empire general tricked into Vampirism who, though shunned by his people, still fights for the Empire using its fallen soldiers to fight after death like he does... or a necromancer driven to swear an undying crusade against a people... the possibilities are endless. You can make the story as detailed or personal as you like, or be lost in the waxing and waning of the diabolical plans of the Von Carsteins.
Dark Elves have a very specific place, and it's hard to carve out a special place for them outside the defined background or cliche ideas. Demons are even more locked in, as each God is pretty much established iconic lore. VC offer the most flexibility here.
The Gamer
This person has a playstyle and chooses the army based on it. Be it they like the idea of an endless horde, an army that has potent sorcery, or a very aggressive combat geared army... they know what they like and they take it. Not necessarily "Win-at-all-Costs"... they just like a certain style.
Vampire Counts have a very flexible list, much more so then Demons (especially if you go a certain style/theme), and I'd argue more so then Dark Elves. The Vampire counts can go (off the top of my head): Horde, Cav heavy, Solid infantry blocks, aggressive, bunker, and elites. A nice variety of troop choices. Little shooting, yes (aside from the banshee scream, which is even nicer in the new book).
We are a strong army yes, but tactical use of the troops pays dividends. VC are somewhat more reliable as they don't fail psych tests. So they're more likely to do what you tell them too... or not run from a very tightly fought combat. You have a better idea of what to expect from them. Which helps make better plans too.
also there's the cash factor
VC allow you to use up your bits. Need another 20 zombies? Get all those extra arms and heads and have them getting out of the grave. Perfect for zombies that you raise. Have left over skeleton bits? Excellent... skeletons coming out of the grave. If you plan ahead you can really stretch your dollar/pound/euro/yen. Conversions can also make for cheaper figures too... I used handgunners for my spirit host... and you can almost use anything for spirit host! Black Knights? Get some plastic knights of another army and convert them up!
VC armies, despite appearances, can me made much cheaper.