The Pre-Dawnguard Vampires resemble the more classical vampires you've reed about in literature; Dracula, Carmilla, Lord Ruthven, etc. They blended well into society, but struck at night to drink the blood of the living. Although the pre-Dawnguard vampires don't have super-human strength, they follow this version of vampire to the 'T'.
The baser vampires in Dawnguard are the same as before, minus the Vampire Lord form. The only difference is that you have the option to join the Volkihar vampire clan. If you get infected by a random vampire in Skyrim (with or without the Dawnguard DLC installed) you'll be a pre-Dawnguard Vampire no matter what. However, if you accept Harkon's gift, his Blood, then you'll become a Volkihar vampire with the ability to turn into a Vampire Lord, which is a huge upgrade in terms of Power and Abilities.
As a Volkihar vampire, in your baser form, you'll have the same abilities as the pre-Dawnguard vampires, but you'll notice a drastic change in appearance (which I think is awesome). You'll be noticeably paler, more corpse like. Your eyes will change to a reddish-orange color and in the dark, you'll see them glow. The Vampire Seduction power (which you get at Stage 2) has been upgraded to allow you to feed on NPCs while standing up which can eliminate ever feeding on sleeping NPCs again.
The fun begins once you change into a Vampire Lord. There, your appearance will resemble a demonic bat out of hell. You can hover over water and travel across the land at great speeds. You'll get a separate Perk Tree that gives the form more power and abilities such as Summoning a Gargoyle, Mist Form, Bats, Blood Magic, etc (all which you achieve by using your Blood Magic or Power Bite to gain Perks). You can also fight on land, like a werewolf, using your Talons. You have the best of both combat styles, Magic and Melee, rolled into one. The best part is that the form can be used at will. No time limits. Just revert to your baser form and change back whenever you want.
The weaknesses for the vampires are the same, yet the pre-Dawnguard vampires suffer the most. Fire, Sun and Vitals Regeneration are all still key elements in planning for questing and the longer you don't feed, the stronger your weaknesses get. However, your powers grow stronger the longer you starve yourself. One of the best things about joining the Volkihar vampire race, besides the perks and form, is that Stage 4 no longer affects you. As a pre-Dawnguard vampire, if you haven't fed on blood for 4 days, you will become Hated and Feared. Every NPC will attack you on sight. From the sweet old woman in Whiterun to the crappy guards. They will attack and kill you. You will have to feed on a sleeping NPC just to get back to Stage 1, which can be hard if you have trouble sneaking into a town at night unnoticed. Volkihar vampires don't need to worry about this. They can go on questing and not feeding without the worry of the towns folk attacking. Although, your vulnerability to Fire will be high and the sun will stop all vital regeneration and cut your vitals almost in half. The cover of Night is Haven to all Vampires. Caves work well too.
If you want a more classical vampire experience, don't become a Volkihar vampire. As a vampire fan, I enjoyed the classical approach to my favorite mythology. However, in a video game, even that can get tiresome. The Vampire Lord offers a more versatile and deadlier vampire in Skyrim. From the absence of Stage 4 to the freedom to change into a Vampire Lord at will, wielding all it's powers, it'll be hard to stay a pre-Dawnguard vampire in a Dawnguard world.
Hope this helped.