BJT vs FET for VHF LC oscillator
What would be the advantage of a JFET (e.g. J113) over a BJT (e.g.
  MMBTH11) for this application? And why the preference for an emitter
  follower topology?


I've run common-collector Colpitts oscillators using BJTs from sub VHF to 600 MHz and there is no great problem to be found. I prefer the BJT because there are more options to choose from and JFETs appear to be not as much in favour as they used to be. But, the reduction in component count will be significant to some designers so it shouldn't be ruled out.

As to why the common-collector Colpitts oscillator is preferred is down to Miller capacitance - the collector is not used hence it does not force negative feedback to the base and cause problems. Loop gain comes from the voltage amplification due to C3 and L (Colpitts A) and the oscillation frequency sits on the slope of the resonant peak.

It's the same answer for a JFET - miller capacitance is constant and drain amplification is zero.