[MyNameIsNigel]

According to AutoHebdo, the performance of the Audi R18 at Spa was hampered mainly by two issues:
(i) the simulations suggested that the LM-spec car would be faster by 0.5sec compared to the sprint package run at Silverstone, but these simulations were assuming much cooler track conditions; the LM-spec packaged turned out to be less adapted to the hotter conditions. Interestingly, Audi were originally contemplating to race the two different aero packages at Spa, but this plan was changed after Silverstone;
(ii) Audi opted - like Porsche - for two specs of Michelin tires, soft tires for "cold" temperatures (< 17 degrees C) and soft tires for "hot" temperatures (between 15 and 30 degrees C). Both tires specs happened to be unoptimal for the actual track conditions. Toyota were the only ones amongst the manufacturers to opt for soft tires "hot" temperatures and soft tires for "hot +" temperatures (> 25 degrees C). This explains the good level of performance of the TS050s at the beginning of the race (Buemi's double-stint as the beginning of the race was apparently made using the "hot +" tire compound).

It's worth noting that the manufacturers had to make their choice of tire compounds for the Spa round back in early April. Toyota's choice at the time was quite bold and happened to be spot on. This should also be taken into consideration when analyzing the level of performance of the three manufacturers.