As a rotator at both places, I'll help you out as much as I can.
Biggest difference is inner city (Drexel) vs. suburban community hospital (Monmouth). So, lots of trauma vs. NO trauma (unless you consider the 80 y/o lady falling & breaking her hip trauma). 4 residents/yr vs 2/yr. But, about half the residents are away from Hahnemann while Drexel residents mostly rotating at Abington 30 minutes away where you do all of your elective surgery (joints & spine). Never been there, but told it's a good operative experience. Hand, Foot & ankle, & Peds are at other hospitals (St. Chris & Shriner's for Peds at Drexel). You go to CHOP (80 miles away) for Monmouth (but they put you up in Philly). Both have a nice set of residents, with laid back, cool guys. 3 females (1 Chief) at Drexel, 1 female (Chief).
Monmouth is big on rotators. Operate early. All community orthopods. Mostly NYC or Philly trained. Tons of joint & spine (I think there are 5 or 6 spine attendings). Minimal didactics, minimal research. 1 full clinic day/wk. Day procedures are lacking (sports, hand, etc.). Spend 5 months at Morristown (60 miles away) doing (Level II) trauma where they put you up. Supposed to be a great experience. Spend 1 month in NY doing Tumor (again, they provided housing) where you operate with Dr. Canand.
Drexel has a lot of home rotators (3 of 4 last year from Drexel, usually 2 of 4). Good mix. Daily didactics. Spend a lot of time at different hospitals. Both sets of residents round together. Just in case you're torn...PGY-1 at Monmouth has 6 tough months of G-surg where I heard Drexel's is a little better. If you have any other questions, PM me.