Would the sox go P, P, P? Or would they mix in a position player? Either way, I expect the sox and the yanks to have dichotomous strategies. I think the Yankees will select the best position player on their board with their first 2 picks, unless a pitcher falls who is head and shoulders above the remaining hitters. After that, the Yanks will select power pitching. This is what they do. They find big college relievers who have high spin rates and deep (for relief) arsenals who could move to a starting role OR they get guys who started who weren't from big name schools (Dalton Lehnen from D2 last yr who is dominating A ball right now). They'll be pitching heavy in the top 10 as they always are, but they will be top heavy with position players, maybe even their top 3 picks.
I expect the sox to draft a pitcher first unless there is a close to finished product offensive player available who is better than the SP. Pitchers rise faster than hitters and the sox desperately need their picks in the first 3 rounds to rise. They'd prefer to put their first two picks into the long season leagues and see if they can hit AA some time next season, which would put them on a prospect map and in position to land someone of consequence to fill holes that come up.