So, I think I might be able to give you the best comparison yet since you are currently driving a Jetta. We just bought a 320i for my wife last month and we're loving it so far. Here's the rundown of the two cars:
Her old car:
2011 Jetta SEL w/ Nav,Moonroof, Heated Seats, Manual Transmission
Monthly: $336 (12k/36 month lease)
New Car:
2013 320i w/ Sport, Lighting, Premium, Heated Seats, Enhanced BT & USB, 6sp MT
Monthly: $422 (12k/36 month lease)
Overall, the 320i is worlds better than the Jetta was. On the inside, it's so much more refined (obviously) and is better in every possible way. My wife absolutely loves it! The 320i has quite a bit more power than the Jetta SEL and it is very noticeable. I have been driving the Jetta as my daily for a couple months until my new car comes and it's brutally slow by comparison. The 320i is somewhat underpowered as BMWs go, however. My last car was a 2011 128i and it was a lot quicker than the 320i.
The handling on the 320i is way better than the Jetta (definitely get the Sport pkg). The xenons are SO MUCH BETTER than the Jetta's lights. It's like driving in the daylight.
The 320 looks really nice w/ the sports package and the 18" wheels look pretty rad in person. I wasn't a huge fan of them on the configurator, but they look awesome in person.
The missing HK sound isn't that noticable to me. I had HK in my 128i for 3 years and I can't really notice a big difference between the 320's stock sound. I'm sure if I had the windows up and a CD in, I could tell.. but I don't think it's a big concern.
As a replacement for the Jetta, the 320i is hard to beat for the price. You can save thousands compared to a 328i equipped with lighting and sport packages. If you decide to get the Premium Pkg on the 320i, you can close the equipment gap between the 328 even more. If you are used to faster cars than the Jetta, you may want to test drive the 320i to see if it feels too slow for you. It's faster than most normal cars, but it's not exactly quick.
Feel free to ask me any other questions and I'd be glad to help!