One of the biggest problems with Bitcoin is that the whole network can be controlled if the mining becomes centralized. Unfortunately, this is the reality today. Two mining companies in China control over 50% of all of the hashing power on the Bitcoin Network. That means that Bitcoin can never advance technologically, unless those two mining companies decide to allow it.
The creators of Vertcoin made it a top priority to create a coin in a way that the mining could never be centralized. When the mining is more fair and equally distributed, then the decisions that need to be made about the future of the coin can be made by the community as a whole, and not by two people sitting in a room.
Since there network is not controlled by a small group, they have the freedom to add new innovations such as "Stealth Addresses". Stealth Addresses enable people to exchange funds privately. This may not sound like a great acheivement, but very few coins can provide a way to make transactions completely anonymous.