Does handwritten speech indicate anything?
I read the VIZ translations and from what I can understand, the handwritten speech denotes 'drowned-out' dialogues. During this time, the character, Emiya, seems to be in an internal monologue. This is meant to tell the reader that the focus or the important parts were not on his 'drowned-out' (the handwritten ones) dialogues but rather on his internal monologue. 

This is also seen in an anime where the character is thinking to himself/herself. The scene around the character would have its volume lowered down (but still hearable) to give focus to what the character is thinking.