Although men and women are built differently there is no reason why they have to have significantly different weight training routines. Generally women have substantially less muscle mass in their upper body than men, due to their genetic make-up. So an upper/lower body split is probably more appropriate than including a whole lot of upper body strengthening days. However there doesn’t have to be a difference in training volume, sets and reps etc., this should be dependent on training goals.
Women are often a little paranoid that doing weights is going to cause them to bulk up, this however is somewhat of a fallacy. Only women with a predisposition for muscle growth will see a substantial increase in size. A lot of women have the primary goal of toning up, which is basically achieved by gaining muscle and losing body fat. Weight training is a highly effective way to lose body fat, as an effective routine will allow you to gain muscle, which in turn raises your metabolic rate (the more muscle you have the higher your metabolic rate will be).
Contrary to popular belief, not all resistance exercise improves or maintains bone density. For the bones to get stronger an adequate amount of stress needs to be imposed to cause adaptation and subsequent growth. Lower reps with heavier weights are going to be much more effective at giving your bones the stress they need to adapt. Lower rep compound exercises (multi-joint movements i.e. bench press, squats etc.) also burn more calories, so are more effective from a weight loss perspective as well.