I clean the veterinary office I work at. We don't sweep... we use a high powered vaccum for all the non-carpet floors. Works MUCH better than sweeping. The few times I've tried to sweep (vaccuum out of order), I still found hair everywhere afterwards. ICk!
Most of the time at home I will sweep all the dirt, hair, etc into a pile, and THEN bring in the sweeper. I'm sorry, but trying to broom dirty and debris into a dust pan ALWAYS leaves little particles of dirt behind in a small thin line. ICK! So, I do a mixture of both!
Oh, and when it comes to bathroom floors, .. I don't like mops much. When it comes time that they actually need cleaned, I get down on all fours and scrub the old fashioned way. IMO, it gets the floor the cleanest, unlike the mediocre job that swiffers can do. Nope, give me a scrub brush, a bucket of hot soapy waters, and some tunes to scrub to.