I feel like I can weigh in here a bit, having had a BMW M-Sport F30 320i (184 hp) and now a Audi A4 B9 (190 hp), I probably have good grounds to compare.
Audi is obviously better on the interior. No question. The BMW interior squeaks upon pushing the dashboard trim, and even when driving there are subtle, yet annoying vibrations and squeals. The tech inside is far superior than the BMW (although, I guess the Audi is newer) But the BMW doesnt even have bluetooth music as standard? A ****** Hyundai i10 has bluetooth as standard, as far as I know.
I had more gripes with the Auto Stop/Start of the BMW than the Audi. My Audi only does it when my aircon is either off, or above 18 Celcius, which it seldom is, because its hot AF in South Africa. The BMW did it always and it really felt like it was putting strain on the N20 engine inside.
Exterior wise, its each to their own. Both were beautiful for their own reasons. Though, where I live, everybody and their kid that has a 3 series wants to pretend its an "M" car; so theirs that. Its definitely more of an "immature/nu-money" car.
The A4 is more refined, and in terms of "sporty-ness", leaves a bit to be desired. I've gotten the same amount of head-turns/looks in both, if that counts for anything.
And now for the nitty-gritty. Driving experience? BMW wins. No contest for me. The RWD vs my FWD now, was a lot better. (Cant attest to the Quattro. I'm sure that's better..but there's no snow by me so i didnt feel necessary). The Audi is more refined, and "solid" feeling, but in the BMW I felt way more confident in overtaking/pulling off, and didnt have that throttle lag I experience now.
I'm no racer-car driver, so it doesn't matter to me all that much. I'd pick my Audi over a BMW F30 again, but if it weren't for me hating the exterior of the BMW G20, I'd consider moving back to BMW...... Though my friend just got a Golf Mk7 GTI and that thing looks like a lot of fun.