Like Cdog says, in most cases the original bullet for caliber is usually best bet, if shot at same velocity. Even though 44sp is lighter than 44mag the 240gr cast is hard to beat in 44s for 1 bullet fit all. I’ve always found that going to lite side sacrifices accuracy.
I just loaded 44sp with 214gr HBWC, if this doesn’t work out the HB inserts can be removed for solid WC that is about 240gr.