Since I own a Bianchi Eros Donna, I'm rather partial. That said, while researching road bikes to death when I was on the hunt for one, I adopted two essential "rules." First, buy the bike that fits the best, without getting too wrapped up in components. In particular, try to determine whether you feel too cramped or too stretched out on the bike based on the top tube length and stem. Have you had a bike fitting or are they just having you stand over the bike to see if it fits? Also, do you like how one bike "feels" over another? I'm assuming both of these bikes are aluminum, but might differ considerably in ride quality.
Second, unless you know for sure that you're going to buy another bike in the near future, buy the best speced bike that you can afford (including the wheelset). Assuming fit/feel are roughly the same for both the Bianchi and Giant and that you can afford the Bianchi, that's the bike I'd buy. While the difference between 105 and Ultegra may not be discernible to you at first, over time, you'll probably be happier with the Ultegra components. If you went full Ultegra, you would like not feel the "need" to buy another bike any time soon.
Either bike, however, would likely serve you well.
Good luck.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher