If you are a fan of GC2 I would recommend buying the beta, if just to save the $5. The beta is very playable, but not challenging yet. The AI is still very primitive which means even with major advantages it struggles to compete. Major elements like battle viewer and diplomacy are not yet in the game. I would say GC2 is still a much superior experience except for the ship designer which already blows away the ship designer from GC2.
Major updates in the current beta are:
Graphics: GC3 is a much prettier game that GC2.
Ideology: Ideology is now a separate system rather than being integrated with tech and research.
Hex Map: Map is hexes in instead of a grid. This allows balanced movement and looks cool.
Adjacency Bonuses: All improvements grant bonuses if certain other bonus types are built near them, making planetary development much more interesting.
Shipyard: Ships are built on off-planet shipyards that can be sponsored by multiple planets.
Strategic resources: Asteroid mining and the old resources of GC2 are gone, replaced by Durantium, Anti-matter, and Elerium, which enhance weapons and defenses. They are mine-able by starbases.
Better control over the economy: Economy now runs off population and is completely customize-able at the planetary level.
Tech Ages: The tech tree has been divided into ages, forcing players away from narrow specialization to a degree.
Major updates not in the current beta:
Ship roles: Ship combat will be more involved, with the ability to give some basic orders at the beginning of combat. They haven't given us too many details on how exactly this will work.
Galactic Congress: There haven't been too many details, but they've said it will have more of an impact and you will be able to propose legislation.
Stuff not yet in the beta:
Political parties
Diplomacy
Combat viewer
trade
Cultural or scientific victory
Espionage (wont be in release, has been promised for an expansion)
AI that can play the game well
Custom Races
I'm sure I'm forgetting a ton of stuff, but that's what comes to mind at the moment.