What is the advantage of long baseline neutrino accelerators, with respect to short baseline ones? What is the advantage of long baseline neutrino accelerators, with respect to short baseline ones ?
Let me clarify :
with long baseline, there is important MSW effect from travelling earth. There is also the spread of the focusing of the neutrinos with long distance. All these drive to uncertainties. There is also the cost of big logistic to have two detectors at >100 km distance, for people in a same Community (money for transport for people of the collaboration, etc.)
Why with short Baseline, all these problem don't exist.
Since the important parameter for exploring neutrino phase space is L/E, why just increase the requested energy of the neutrino, from the selection at the production site. In this way, we have a reasonable distance. 
(The only drawback that I see in the increase of energy is that the separation of pi/kaons (that produce the neutrinos) will be worst, so that there will be a bit more contamination from antineutrino in the neutrino source.)
In addition, it seems, from :
Why does the Neutrino cross-section increase with energy?
that with increased Energy, we would have increased cross-section.
So what is the advantage of having long baseline experiments accelerators for neutrinos ?
 A: If the physics is best studied with L/E roughly 600 km/GeV (see discussion by @Zeick) then let’s compare two choices


*

*1 GeV scale beam means a 580km-scale distance to a remote target

*a 1 km scale distance is a 1.6MeV (not GeV!) beam
That low-energy beam has a lot of practical difficulties:


*

*the target cross-sections will be low, so high intensity is needed (although you gain with the closer target, you don’t gain enough; see below)

*the beam will be much wider, which is another intensity issue: high-energy beams are kinematically focused by the large forward boost momentum vs smaller transverse interaction momentum. At low energies, that’s not there. 

*the (fractional) monochromicity will be much worse: the (fractional) energy spread will wash out results


Plus various difficulties associated with intense low energy beams, etc.
So the practicalities of doing the experiment mean that long baseline is hard, but short baseline for that physics would be even harder. 
A: Long-baseline neutrino oscillation experiments (loosely defined by source-to-detector distance $L$ > 100 km) are needed to measure the CP violating phase of the lepton sector. This is done by measuring the difference of probabilities
$$
P(\nu_e \rightarrow \nu_\mu) - P(\overline{\nu}_\mu \rightarrow \overline{\nu}_e),
$$
which is zero if CP is conserved in neutrino oscillations. If one calculates the expression for this probability difference with the help of the current knowledge of neutrino mixing matrix (PMNS matrix) parameters, from Nu-Fit.org or somewhere else, and extremizes it with respect to $L/E$, the baseline-to-energy ratio, one finds that the first maximum of the probability difference is at around 580 km/GeV, and this effect is quite small, around 2-3 %.
Since neutrino energies in accelerator experiments are approximately 1 GeV, the baseline (source-to-detector distance) should be around 580 km - which is the distance of a long-baseline experiment. Any short-baseline experiments would be very inefficient on measuring the leptonic CP phase. It is probable that DUNE and Hyper-K will both independently measure the phase during this decade. The early hints have ruled out the CP-conserving case within 90 % confidence limit, but only time will tell if this really is the case.
