To answer the OP, the main advantage of compensating designs is the reduction in weight.
This gives a quicker playing response time, the possibility for a lighter and more transparent sound and a less tiring high register (when compared to the equivalent "full" design).
Some compensators do indeed have good low F-sides and should be considered as serious instruments.
However, the low F-sides of the best full doubles also feel significantly better (more even reponse, richer sound, etc) than the low F-sides on good compensators.
Compensators are an interesting choice for solo, chamber and orchestral 1st playing, where the advantages of a "fast and whizzy" horn can outweigh the disadvantages of a slightly less good low F-side.
Obviously for orchestral 4th playing, the choice would be different - it depends what you need to do.
After spending time on several horns (from Bb single to full triple), my personal preference now is for a relatively lightweight full double (2.4 kg) which manages to be both "fast and whizzy" and have a great low F-side.