Differences I can muster:
1) The Quadra is traditional RAID, so you need all the drives to be of identical capacity and spec to work or you'll just be wasting your money. Drobo allows you to combine any mixture of capacities and you can format the drive as a 16TB volume, so you need more space and bigger HDDs come out, you can just swap existing drives into the enclosure to expand you space.
2) Quadra: Standard RAID, means you can just take the drive from within the enclosure and pretty much read it on any other computer. Drobo: Proprietary solution means you cannot read the data on the disks on another computer; you can however use them in another Drobo.
So if you are planning to buy either, you need to balance your needs. Drobo is good if you have a bunch of disks right now that you can fill up as you go and then in future buy new drives and then keep adding to the capacity.
However if you are going to be replacing you enclosure in a few years, you don't see yourself upgrading the capacity, the Quadra will be a better choice. Also since it has eSATA you can technically run 2 Quadras and RAID0 in each (for performance, and then RAID 0,1,5, etc between those Quadras and benefit from space expansion like that.
