In a way your question is like asking which is faster, 2008 Camaro or a 2015 Ferrari. The answer is all depends. If you intend to use both to get around town in Manhattan it doesn’t matter. A 1965 VW Bug would be just as fast. If you intend to drive on the Autobahn the Ferrari is going to be faster.
The 2015 MBA has a much faster bus meaning data passes to and from the CPU at much higher speeds. The CPU of the MBA is fully 64bit while I believe I’m correct that the 2008 MBP processor was 32/64 making it slower by comparison. Both may have SSDs but the MBA will read and write to its SSD significantly faster. In short, the MBA is the faster computer. But...
A 2008 MBP is no slouch, even now. For normal usage (browsing, word processing, etc) its major bottlenecks are 1) relatively small amount of RAM and 2) its mechanical hard drive. But by installing an SSD you’ve ameliorated both issues. (Installing an SSD in my 2009 MBP gave it an additional 18 months of life for my needs and the person I sold it to is amazed that a 6 year old computer is faster than the 3 year old PC it replaced.) If your needs are modest you may actually notice little difference between the two. When I bought my current 2015 rMBP (much faster than my 2009 MBP) it wasn’t until I used Photoshop to open up a set of RAW photos from my camera that I began to realize how much faster it was. But when I’m doing email, writing, and the like I don’t notice a difference at all.