Like many others, I prefer to mix mono tracks. Mono tracks make it easier to get a more satisfying stereophonic width in the overall mix.
This can be a challenge when you use synths and samples, which normally default to stereo. Sometimes, converting them to mono results in information being lost or a thinner sound due to phase cancellations. You therefore have to approach each source individually rather than applying any fixed rule. I'll fold most stereo sources to mono and listen for any tonal degradation; more often than not, there is none.
Except in special cases, there is little value to splitting a stereo track into dual mono. It does give you more panning options, but Channel Tools does that without the bother of splitting the track. I do, however, split piano much of the time so that I can process the left and right hand parts separately.