Of course I’m speaking more around the time of the crusades than in current modern history.
I seem to recall the naval battle of Lepanto where a slightly outnumbered joint Christian fleet of the Holy League defeated the mighty Ottoman navy.
The majority of times that I have read accounts (for example, those made during the Second Crusade), they always hint at the numerical superiority of the Muslim forces involved, and this is even so when the battle was won (by the Christians/Byzantines/etc.).
So how many battles have there been where an outnumbered Muslim army/navy defeated Christian forces, and did Muslim forces regularly bring more soldiers to battle than did thier Christian/Western counterparts?
Well pre-modern I can think of a few off the top of my head:
Jarbiya-Yarmuk, 636 - The key engagement that shattered Byzantine strength in Syria during the initial Muslim conquest. Contemporary troop estimates are highly unreliable, but most scholars agree it appears the Byzantine forces enjoyed some sort of numerical superiority, though how much is hard to say.
Transductine Promontories, 711 - Again, part of the early conquest period, this time the key battle against the Visigothic state.
Azaz, 1030 - An obscure one. Emperor Romanus III, ruling the Byzantine state at the peak of it’s military prowess ( and the beginning of its decline from that peak ), fascinated by all things military, decided to take an opportunity to punish the local Emir of Aleppo ( a minor ruler precariously balanced between greater powers ) for border incursions and personally lead a large army against him. The Emir caught him in an ambush in a narrow defile and by galloping a small force of horsemen back and forth across the Byzantine rear while the army was bottled up, panicked the Byzantine force to the point where the whole army simply routed and fled.
Marica, 1371 - A key victory of the Ottomans over the Serbs, almost certainly more important than the more famous Kosovo-Polje in 1389.
Preveza, 1538 - The earlier counterpoint to Lepanto, where a smaller Ottoman fleet outmaneouvered and defeated a larger Christian armada.