Dash takes the most popular / trusted anonimization usage from the real world today (BTC tumbler) and makes it integrated / faster / more convenient / trustless with no 3rd partys.  Then it's ahead-of-time tumbling so you don't have to wait to mix with other anonymous transactions like Cryptonote (which is also unproven in the actual market due to it's lack of practically any adoption/usage).

Second the tech to do this (masternodes) provides an incentivized second-tier of fullnodes that can then be used for a lot of new uses not possible with Bitcoin's single-tier voluntary service provider approach. Features like instant transactions (transactions locked in the MN tier without having to wait for the next block) and decentralized governance / funding for coin development and pruning/abbreviation to prevent bloat and likely lots of use cases not envisaged yet, all provided by tier of (currently 2800+) fully hosted / maintained servers operated by the coin users themselves.  

The high value today compared to most other alts is a reflection of the potential value the market sees for the Dash 2-tier technology that positions Dash to capitalize better on opportunities and demand coming out of the ongoing merging of crypto currencies into main stream applications and services as the whole space matures.  In other words, 2-tier architecture is a much more versatile and flexible approach that provides a lot of added value, and is unique to Dash so it has the first-mover advantage.  This coupled with the track record of consistently delivering working features as planned with a very professional and busy dev team and the large community / ecosystem forming around it.  And has some of the most involved ongoing development of any coin e.g. https://dashtalk.org/forums/testing.53/ which is prerequisite to providing confidence it can succeed in delivering a value-add over Bitcoin from a technological perspective.

More details on the anonimization features from the main dev: https://soundcloud.com/mindtomatter/ltb-e196-distortions-towards-privacy-or-many-hands-makes-light-work