Do women get the same benefits from exercise as men do?

Yes. Women and men alike benefit from exercise with improved stamina, increased strength, and improved weight balance.
Yes. Exercise is an important way for women and men to achieve optimal health. Some women shy away from strength training because they're afraid they'll get bulky manly muscles, but it won't happen. Men and women should work for a balance of fitness including cardio, strength, endurance, flexibility and body composition.