I used to obsess a lot about specs, but I've shifted from buying the equipment that looks the best on paper to getting the equipment that makes me smile when I use it :-) I know it's an oversimplification, but even with specs, you make subjective decisions on what kinds of measurements to favor, or what frequency plot looks the best. In the end, all that matters is how well YOU think it works for you.
So here's my buying philosophy now: Pick a couple of audio interfaces within your budget range that looks appealing (professional reviews as well as products with many consumer reviews on e.g. Amazon are often good pointers if you don't know where to start), then borrow the equipment or buy it under a 7/14/X day return guarantee. Bring it home, make sure you have some interesting things to record lined up and see how you like the sound.
When you make test recordings, try to record the kind of things that make you think your current equipment is not up to the task.
Then buy the one that you think works best in your setup. If they all sound great, then you'll probably have a favorite in terms of ease of use or most options, etc.
Oh, and don't forget to compare with your old gear. Maybe the new gear wasn't actually what you really needed to improve your sound?