I have had one natural birth, and 3 c-sections, and i can tell you, I bled alot less with the natural birth (as you only have the placental wound on your uterus's insides to heal, yet with the c-section, you have the cut as well).
The loss I had with the c-sections was heavy for about a week, and lasted for 5-6 weeks, before finally leaving. With the natural birth, I stopped bleeding after 7 days!!
And yes, after the c-sections, i needed to sit down whilst having a showe, and while getting dressed, as I was so damn dizzy and unsteady on my feet for about 2 days.