"Bob resented his father's criticizing..." is the grammatically correct one. In this sentence "criticizing" is a gerund, a verb form that functions as a noun. In this sentence it is the object of "resented" and is modified by "his father's"

Thank you. James!

Some (I repeat: some) people see a difference in meaning. Here are two examples that I found in a good grammar book: 1. Mr. Smith disapproves of Tom's marrying his daughter at this time. = The emphasis is on the marrying. Maybe Mr. Smith feels that his daughter is too young. (Although Mr. Smith might like Tom very much.) 2. Mr. Smith disapproves of Tom marrying his daughter. = Mr. Smith does not like Tom. He does not want his daughter to marry him. ***** If you accept this theory, then maybe your sentences could be interpreted this way: 1. Bob resents his father's criticizing the plans. = Bob's resentment is directed toward the criticism. (Maybe Bob feels that his plans are excellent and that no one should criticize it.) 2. Bob resents his father criticizing the plans. = Bob's resentment is directed toward his father. (Maybe Bob feels that a father's job is to support his son, not to criticize him.)

Bob resented his father for criticizing the plans for his new office building.