Best:
A newly taken city with a skeleton garrison in it, I had just taken something else and had stocked it with my best troops, heading back with my 9 companions and about 20 low-tier troops. I saw the besieged city with an army of 100 sitting outside, and I knew that if I got in, my 20 + the garrison's 25 would be able to pick off that army if they attacked. Got into the city, then 4 other armies turned up, so I ended up facing off against roughtly 600 troops with only 50ish troops. After those battles, city defence is a breeze for me; set up cavalry/infantry right where the ladder came up, and positioned myself to the side of the opening. Using the reach of me double handed balanced sabre and jumping to increase the hit height, I could catch almost every enemy soldier as they got caught on the tips of my companions swords... I think the final wave did break through and I had to break a hasty retreat along the battlements, taking them out as they came towards me, but I did get it in the end...
Worst has to be either being killed off by deserter Khergit Lancers on Day 2, assorted headshots or couched lance deaths from what are supposed to be general policing of my fiefs (desert and steppe bandits do that... ) or completely underestimating Rhodok Sharpshooters when attacking a Rhodok castle. I had an army of 150 Swadian Knights, crossbowmen and some Men At Arms... Completely wiped out by same number of enemy crossbowmen and vet spearmen.