We have an F31 and three children and it is adequate for our needs. It is not much larger than an E9x but is a little bit, bit more leg room in the back, maybe width and of course the tail gate area is really handy.
We have had three child seats across the back in the past (down to 1 now) and as long as you choose them wisely they will fit.
We also have a roof pod for holidays but really only have used it when we head to the airport with large suit cases. Otherwise we can usually fit everything in the back.
I think you'll find the 2l turbo with the 8 speed automatic has similar pace to your 330D, if not a little bit quicker. The way they have set up the torque curve (max @ 1250RPM) it is a bit like a diesel and the 8 speed ZF is a great improvement and changes are very fast. I don't really miss our 335i E91. The F31 is a much better daily and of course you have the reliability of the newer car which is important for us.
I would go the 330i if you can stretch the budget as it has a few revisions but otherwise I believe the 328i is a fine car and should be great buying at the moment. It will also drive very similar to your E90. Of course try to get an m sport.
If you want something bigger again you really need to be looking at a 5 series or X5. Otherwise the F31 is actually still quite a large car.
Personally I'd resist being pulled to an SUV.
You should also head over to the local F3x section as there are heaps of 328 owners. I know there is a potential steering rack issue that you should look out for.
https://f30.bimmerpost.com/forums/fo...play.php?f=415