I always just changed 3 sharps to 4 flats because it was easier to play in that key - don't know why. Also, many people feel it's easier to sing in a lower key, albeit only slightly lower. ;-) As best I remember, you had to watch out for accidentals (a cancelation of the original sharp) when they occurred in the music you were reading.

I didn't know 4 sharps would transpose to 3 flats - I guess it just never came up. (probably not common in hymnals whereas 3 sharps is fairly common) But I do know that 6 sharps is easier to play than 3 sharps - once again, not sure why.