They are both good, but you may like the bissel better. I have the shark mop, had the first one they made and I loved it..they made a new and 'improved' one, and even though it is a good mop, powerful, and lots of steam, you have to push the mop forward for the steam to be released. They designed it this way as a saftey precaution. It's a personal choice in how the mops function, both are good mops. I personally like continuous steam.. probably because that is what I have been use to for a few years...that is my disappointment with shark. Either way, steam is a great, easy, fast way to clean, does a great job.
Ree

I have the Bissel and am very happy with it. I have had it for 4 years and use it on hardwood and tile with excellant results. The Bissel has a trigger mechanism on the handle that releases the steam onto the floor. The mop head turns easily and allows me to get around corners, especially great in bathroom around toilets. The Bissel comes with two terry mophead covers. They are removable and I can toss it in the washing machine after each use.