Well, for me there are just too many areas where evidence of cost cutting is clear. Hard, brittle plastics in some places, coarse textures and a general feeling that the overall fit and finish aren't as good as they should be for a premium sector car. This was noted by several reviewers when the [image no longer available]ubbthreads/images/graemlins/1.gif was launched.
And several reviewers found the contrary.
Autocar on the 118d SE, Test Date 12 October 2004:
"The dashboard is stylishly minimalist, of high quality and intelligently arranged, and it’s comfortably up with the best in the class."
The Car Enthusiast, 2005 120i:
"Interior (4 stars out of 5):
Not as much space in the rear as most of the competition, but excellent fit and finish."
on the 130i Limited Edition:
"The 130i Limited Edition is very well-appointed, with high fit and finish levels complemented by the beautifully tailored leather seats and a host of technological gadgetry, including iDrive and a centre-mounted navigation screen; all of the creature comforts you would expect in a car that breaks the £30,000 mark. The cockpit is a bit confined (especially at the rear), but the tactile quality of the dashboard and centre console - angled toward the driver - is at a high standard."
John Simister, for Independent Online, on the 130i M Sport:
"Inside, rear passenger space is tight and so is the boot, but it's undeniably well made and expensively trimmed."
Auto Motor und Sport Sweden have compared the 120 to the A3 twice (both petrol and diesel versions), and each time gave both of them the same ratings for the interior. Autobild scored the 130i at 15 points out of 20. The S3 demolished the BMW...with 16 points.

Similar results in AutoZeitung (185 points to Audi 2.0TDI, 183 points to 120d). There's probably a whole bunch more like that, and quite obviously more so for the face-lifted models and the 1er coupe, but I think that's enough for now.
So, to say that the A3 is far ahead of the 1-Series in interior quality, or that the 1 Series is somehow flimsly while a similarly-specced or -conditioned A3 isn't, sounds like hyperbole of splitting hairs: the A3 may be better, but it's not a world of difference better. Styling is very subjective, and I personally find the A3 interior dated, its upper dash combining with the center console in one piece not attractive. Not to mention many of the hard plastics in the 1-Series can be replaced with aluminum (just as in the A3). I do agree that the exterior styling of the A3 is more instantly palatable, so is likely to appeal more to those of a primarily aesthetic bent.