Both are great cars. I came super close to leasing an A4, as we've had good luck with our '16 CPO A3 (ironically currently in need of a water pump). I regularly flip between said A3 and the Giulia, and they are hilariously different.
The Audi feels like transportation that has been broadly optimized to have zero pain points. It checks all the boxes, from comfort, composure, passing power, and tech. They're great vehicles for covering lots of miles. The seats and touchpoints are top of the class and wear amazingly well. The styling is conservative enough so that no one really judges you one way or the other. The handling is capable but numb. Basically B+ across the board. You will love it the first week, like it in 6 months, and it will graduate to being a "good, upscale car" after a year.
The Giulia was designed for handling, first and foremost, which is why it feels like nothing else in the class. It has immense dynamic capability, that took me a few months to really explore and get to know. I liked it the first week, loved it after a few months, and 6 months in am just totally obsessed with it. It communicates well enough to make the Audi feel like a dump truck, but somehow does it without ever beating you up. The touch points are fine, not great. As is the interior volume. As is the tech. I personally never really notice though, as Android Auto works fine and I am just always having an absolute blast. It's like how you never remember the bad parts of your vacation. ALSO LOOK AT THE **** THING. My only regret is leasing instead of buying.