Jerry, there is an interesting discussion about this very subject going on right here:
In wet conditions, they don't perform equivalently when you're hiking with a hardshell on. You'll be suffering with a synthetic layer under even the most breathable hardshell. In drier weather, I wholeheartedly agree with you that a synthetic layer is more valuable than fleece. When you're dealing with freezing rain/sleet, you're going to need something under that hardshell to keep the warmth...and a fleece performs better than a synthetic layer.
Ken, if you ever decide to up your budget to 80 dollars, nwalpine.com makes some great hooded fleeces. They are a cottage manufacturer which changes their products constantly. Right now they are offering a lighterweight fleece hoodie (called the Black Spider Light, but before that they were selling a Gridded polartec powerdry hoodie (Called the Black Spider Hoodie). It's like a Patagonia R1, but with a better fitting hood, and its made in Oregon.
It looks like this:
If you are firm on your budge, the eddie bauer/first ascent cloud layers are on sale for 30 dollars right now. They are only 100wt and don't have a hood. Also, I think the clymb.com has cloudveil on sale right now...they are selling a powerstretch quarter zip fleece (model is called "run don't walk") that is in your price range. Let me know if you need an invite to theclymb.
I also agree with Steven, if you can, go with a gridded fleece.
The Melanzana hoodie is almost in your price range. Not as close-fitting as the NWAlpine