Currently, BJTs are more linear than MOSFETs - no contest. This may soon change with rapid advancements in lateral FETs but so far, the BJT is overall the most linear you can get. There is information on this topic in previous threads where I went into some detail on this point. This is why BJTs are most often used in amps actually. One of my research collegues is currently developing new doping techiniques in lateral FETs to improve their linearity and I have discussed this with him in detail.
FETs tend to be less stable but they are thermally better and can be used with little feedback if the painstaking task of matching them correctly is done. Transistor sound depends largely on circuit design (especially voltage-gain stage) so this point is hard to compare between the two types.
As far as bass control, it depends on the use of the transistors, SOA, and output impedance so it is hard to compare in general terms. Check the archives for more info. Take care - Arthur