The thing you need to know about LFS is the cars do handle differently and behave differently depending on how you drive them. This isn't Need for Speed.
You mentioned you went sliding off and he didn't. His tyres may have been at an optimum temperature. Pressing F9 on your keyboard will display the temperatures for each wheel. Blue is cold, Green is Optimum, Red is hot. The thin band at the top of the wheel is the surface temperature. The thick block of colour is the actual tyre temperature.
Keeping it in the green will give you the best grip. You start losing grip if you go beyond green.
The LX6 is a notoriously difficult car to master. Simply because it is so twitchy. The reason it flings you off the track is because, you put too much lock going into the turn, the back stepped out, you then went to counter steer it. And (I'm assuming) lifted off the throttle. This meant the rear wheels stopped sliding, and you then started turning in the direction of your wheels. (i.e, into the wall)
I would suggest getting a few setups for each car.
http://setupgrid.net/
You'll see on the left, Download All Setups. Just extract all of those into your LFS>Data>Setups folder. You'll see a few in there already. You'll need to tweak one or two of them. As some of the XFR sets are designed for qualifying. So will have a tyre that has a lower optimum temperature. Find a set you like. If you want to edit it a little to suit your cruising needs then you can always do that.
I have no idea what the optimum FFB settings are. I drive Keyboard, always have, seem to get on alright.
You'll eventually get the hang of it.