I have been driving for 8 years for work and studies and I didn't find the need to take public transport for my travelling within KL. Then, for the past 1.5 year I have been taking LRT everyday for work because the location of my office is just too convenient.
Whether to drive or to take public transport, I'd say it's a really case by case basic depending on where you from, where you go to, when do you go and what do you prefer during your journey.
For example if you stay very near to a LRT station or your office is right opposite a LRT station, it doesn't make much sense for you not to take the train - considering the traffic congestion and parking fee. On the other hard, if you need to travel during office hour (say to meet client) then I reckon driving is a wiser choice. One thing I like to travel in LRT because although I have to stand, I could do some reading and studying. Imagine I could take 5 Microsoft certifications mostly in the span of 9 months - thanks to the time I was standing in LRT.
Speaking about Bangkok (I've been there 7 times in this year). I took their train, bus, taxi and even their motorcycle taxi. Again, which type of transportation to choose really boil down to the particular situation. The highway will be congested during rush hours. Driving for 1.5 hour each trip to office is a norm and taking public transport to office for 2 hour each trip is also a norm. BTS is one of the many lines. What I observed is BTS typically connect the areas in city center, while there are other lines such as MRT connect to more of the residential areas. @Mag you are right on people are still open to public transport. But note that very often they are doing it out of choice because many people stay very far away from where they work and driving to work (petrol, toll, parking) is just a little expensive for most working class - not very different from what we have in Malaysia.
Compared to Singapore and Tokyo, public transport is very convenient. Every where I went, the thought of renting a car or getting a taxi never crossed my mind. I have the impression that I could just go anywhere with public transport, in this case it's their trains. This is the effect of a matured public transport system. Unfortunately Malaysia still have some catch up to do. However I'm feeling positive that public transport projects moving to the right direction.
And back to the topic, yes, BRT system will definitely help upon it's completion. Even if such initiative do not ease the traffic immediately, it would AT LEAST help by not making the traffic congestion worse in the future.