Shadow_7, I checked the respective Web sites just now, and found the equivalent noise for the Avenson listed at 28 dBA and the Shure at 16 dBA. A-weighted specifications are of dubious meaning at such low SPLs because the "A" weighting curve was designed to match the ear's response at a considerably higher sound pressure level. Also, A-weighted noise measurements tend to be RMS (i.e. averaged over time) so that they don't include impulse ("shot") noise, which is much more audibly disturbing than smooth, continuous noise.
If you want to add about 10 or 12 dB to those "dBA" numbers, you might get a number that comes closer to what the microphone noise actually sounds like, although that is a rough guide, and the whole point is that any one numeric value for noise will nearly always fall short of a true characterization. And I have to say, while the concern about microphone noise can get exaggerated sometimes, given the amount of noise present in nearly all recording venues (as can the concern about preamp noise, given the combined microphone AND venue noise), 28 dBA for a modern condenser microphone just isn't a very good showing.
On the other hand the Avenson is an omni (equalized for free-field pickup, which can sound a bit on the dull side for indoor recordings that aren't very close to the sound source) while the Shure is a cardioid, so the two types of microphone would tend to be used rather differently anyway, even apart from their noise specifications. There's a certain amount of "apples vs. oranges" going on in this comparison, I think.
--best regards