Hopefully this paints a picture for you. I will have my say though. Basic tier database is something that you should NOT be using for production workloads, its quite obvious with the 2GB limit but worth reinforcing the point. Standard tier is more for your common workloads and premium is designed for high transactional volume where I/O performance is much more important to you – my hunch maybe they are utilizing SSDs? I am not sure but the premium costs are much higher.
There is another service tier called Premium RS (In preview). My understanding is that performance is similar to that of Premium HOWEVER only useful for workloads that can tolerate data loss up to 5-minutes due to service failures. I will probably not use this for production but then again it seems to be nearly half the cost of premium. Choices choices choices.
Two notes with this one. First, these are prices as of when Arun put together the notes; they will probably fluctuate over time. Second, there might be differences in prices by data center. At the very least, though, this gives you an idea of the relative price spread.