Being an ex Supra (Toyota ) guy, funny that someone picked up on it.
I have had the exact same feeling in my supra, the first time I drove my 335i, I thought to myself HERE WE GO AGAIN ! ( I'm not kidding )
In my supra ( which had stock LSD ) I fixed it ( I DID permanently ) by changing the offset on my wheels, I know it may sound funny but that was all I did .
I went from 17" to 18" with wider and much more of-set set up, which gave me the grip, and safe feel of higher speeds.
Saying all that, I'm sure that all these will have a tremendous amount of influence on the way your particular car will track ( drive )
- bushings ( sub-frame and suspension components )
- wheel set up
- tires ( RTF vs non )
- steering ratio
- tire pressure
Here's just my 5 cents