Of course Otani can decide whatever he wants and no one really knows what that will be yet, but the Dodgers could only give him $300K as they are capped, where NY can give him $3.5M:
"Eight teams have the ability to pay Ohtani a signing bonus of more than $1 million: the Rangers ($3.535M), Yankees ($3.5M), Pirates ($2.27M), Twins ($1.895M), D-Backs ($1.87M), Marlins ($1.74M), Tigers ($1.072M) and Mariners ($1.056M).
Conversely, 12 teams are prohibited from giving a signing bonus of more than $300,000 as a penalty for exceeding their bonus pools under the previous Collective Bargaining Agreement: the A’s, Astros, Braves, Cardinals, Cubs, Dodgers, Giants, Nationals, Padres, Reds, Royals and White Sox."
http://m.mlb.com/news/article/260668594/10-storylines-to-watch-this-mlb-offseason/
Also Otani wants to hit and there's no DH in the NL, it's unlikely he will play much OF. NY's DH spot is currently largely open, I don't think that's a coincidence.