The pros and cons are:
With a closing date you may get a higher offer as people try to out bid each other. On the other hand you might put some people off as they may have bid before and lost out so would prefer to hold of for something fixed price or where they can negotiate with the seller. You also then have a bit of an unkown quantity in that you don't necessarily know what position the buyers are in and may be tempted by a high offer that doesn't end up going through.
I would think that as you already have 3 people with offers, you look at the position of each buyer and see how much they are prepared to go up to.
I guess you need to weigh the "known quantity" with the unknown that could deliver it all, or leave you with a pig in a poke.
Never ever be persuaded by the estate agents - they are working for themselves at the end of the day, not you. I have had a few bad dealings with estate agents, I would trust my own instincts more than them, they don't always know what is best.