I bought both as I couldn't decide when they first came out. The 11" would be great for a really light user or a user who is using it as a secondary device. If you want it to be a primary Mac, the 13" is absolutely the way to go.
With the 13" you don't need to connect to an external display to get a lot of desktop space. It is more powerful, and it has better drive options. At $1189 refurbished, the 13" with 4GB RAM, 1.86, and 128GB SSD, it is the best value of any Mac. If you need more drive space then upgrade the drive.
The 11" isn't that much more mobile, but it leaves a lot to be desired in terms of using it solely as a laptop. I personally wouldn't want to use it as my primary Mac... and since I enjoy one Mac solutions, I don't see the point in wanting multiple Macs for personal use. The 13" MBA is completely capable with hi resolution display, and the capability to do anything an average user would want or need.
I don't know about games though... I would assume the 13" with its faster and more capable CPUs (more L2 Cache) is the way to go there too... although both have the amazing 320m.