The photoionization of chiral molecules by elliptically polarized femtosecond laser pulses produces photoelectron angular distributions which show a strong and enantio-sensitive forward/backward asymmetry along the light propagation direction. We report on high precision measurements of this photoelectron elliptical dichroism (PEELD). Using an optical cavity to recycle the laser pulses and increase the signal-to-noise ratio, we determine enantiomeric excesses with a 0.04% precision with a low-power femtosecond laser (4 W) in a compact scheme. We perform momentum-resolved PEELD measurements in 16 molecules, from volatile terpenes to non-volatile amino acids and large iodoarenes. The results demonstrate the high structural sensitivity of PEELD, confirming the spectroscopic interest of this technique. Last, we show how a convolutional neural network can be used to retrieve the chemical and enantiomeric composition of a sample from the momentum-resolved PEELD maps.