The two are complimentary systems: the MRT is a subway and the BTS is an elevated train, so none is “better” than the other.
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Having said this the BTS and MRT are by far the quickest and easiest way to travel around the City. Trains are fairly frequent but still get crowded at times. There are less seats and more standing. The system is already being expanded so expect it to improve over the next few years.
Traveling around Bangkok by taxi is surprisingly cheap - sometimes even more so than the Skytrain - plus, it's comfortable and easy, and the drivers are usually really friendly. Taxis have to use their meters - if a driver refuses to do so, find a different taxi!
IF I had to boil it down - the MRT is faster and more efficient, but the bus network does go everywhere. So for me its MRT when I can and combine it with buses to cover the last bit if it isn't walkable.