Well, I can't provide a general answer (so anyone who lives locally or otherwise knows better should still answer), however I can provide a single experience:
Arriving almost exactly 30 minutes before scheduled departure, we were the last vehicle to be permitted to board the train. Some 6-10 cars were turned away, and presumably made the drive over the mountain passes themselves. This may not be typically however, because there was a wedding party travelling on the train, taking at least a mini-coach as well as 10+ private cars. Of course, it is also possible there is a wedding party doing this every weekend in the summer. No vehicles attempted to board at Podbrdo, but then non would have been able to either.
Useful observations for future travellers
- what with the queueing, then the fairly lengthy boarding process for cars, I'm not sure how much time is saved between driving over the pass to Bohinj
- Most na Soči station is not actually in Most na Soči. It's a little bit futher down the Idrica river, across the river from the main road.
- Most na Soči is situated on an amazing coloured lake. If you have time, stop for breakfast or a coffee there.