Does Dawnguard make any significant balance changes to Skyrim?

The short answer is No, the balance of the game won't be noticeably affected.

Dawnguard introduces a few new things that modify minor aspects of the base game:

• Dragonbone Weapons: With a smithing skill of 100, you can now craft weapons from Dragonbone. The bow has the highest base damage of any bow.
• Arrow Smithing: Able to smith arrows

• Crossbrows: Faster first shot with slower reload time. You can smith an Enhanced Version of this cross bow that ignores 50% of armor. This is pretty huge and all you need is the steel smithing perk.

• The vampire and werewolf perk trees are also available, and improve the base abilities for those factions. These are gained by feasting on the flesh of your fallen foes (aka devouring a killed NPC as a werewolf or killing an NPC with drain life or bite as a vampire lord)

So what you're truly given with the DLC is some interesting build depth for players who enjoy playing as a Vampire or Werewolf, slightly more powerful weapons for those who reach 100 smithing, and a bow substitute that can eventually be improved to ignore 50% armor at high levels, but needs to be earned through Dawnguard questing.

Looking at all the info I think you can reach an objective conclusion that current players shouldn't notice any major balance upsets.