The general conditions we use when applying materials, as you've asked the question, would be:

Manganese is applied in high impact conditions due to its inherent toughness. There are various elemental manganese alloys -- with the higher carbon versions being most suited to high wear conditions -- that balance compression strength and abrasiveness. Higher rates of reduction make manganese the preferred wear material (i.e. 10:1).

I'm unable to respond to the straight "chrome" part of the question. High chrome and ceramic materials are most suited to highly abrasive conditions. The high chrome irons apply to materials with over .4 percent silica content. As that percentage increases, the ceramics become more beneficial. Those materials are considerably less prone to impact resistance, with the high chrome material having a slight edge in impact resistance over the ceramics. In either case these materials are best applied where reduction rates are lessened (i.e. 4:1 in smaller sizes).

There's no one material that's superior -- each has its place.