Umm... Just curious, what size frame of Giant are you considering in the women's model? OK, I am hesitant in posting this because I have not figured out my new ride yet, but I have a Giant 2007 wsd OCR1 that is the twin of the Avail that I might be selling this spring. Just thinking/typing out loud
... (it's a women's size small, btw)
OK, to answer your question... I think both bikes would be ok for solid entry level road bikes...
With the Giant, you are getting a triple for gears. I don't live in the mountains, but I have used it some. I need to improve my hill climbing skills, but I can spin faster than I can mash (in a bigger gear). My Giant is/has been a good bike for me. My issue is that my frame size is too big for me (unfortunately figured out after a good fitting at a DIFFERENT shop). Plus, I knew even when I bought it, I wanted to eventually upgrade frame materials to carbon. The bike I bought was the best I could stretch the $ at the time.
The Bianchi is comparable, but you have a compact there for gears. There is the Sheldon Brown gear calculator if you want to do the math and geek it out, but... the lbs told me a compact you basically lose the lowest gear (from a triple) and the highest gear (from a standard size double). So, it's close. From what I understand, Bianchi makes a good bike too.
Hope that helps.