Negative rake inserts are generally stronger than positive rake inserts and have twice the cutting edges. The downsides to negative rake tools are that they consume more HP and impart more cutting forces for the same cut in comparison to positive rake tools. In general they will be preferred for roughing and material removal (due to insert life) but the increased cutting forces can make finishing a part on size a little tricky (especially for small, thin, long, or unstable workpieces). Negative rake inserts typically come with a heavier chip breaker necessitating a much deeper minimum depth of cut than you might be able to get away with on a positive rake insert.
Each tool has its place in the shop. I keep a CNMG (negative rake) set up for material roughing while most of my normal and precision work is done with positive rake tools.
Nice lathe