When to consider Free or Paid model for website product

If you had an online product that filled a significant nitch, would you let members use your site for free instead of following through on a paid model?

Inline with this question, assume that this site did 80-90% of what similar paid sites did whom charged considerable money to use their services. And that eventually you could make up the 10-20% difference. It was an interesting question posed to me and I thought I would ask the larger audience here to help me think this out.

Interesting aspect of this is that I would essentially be giving away the goods for free and would drive a lot of traffic to my site. Plus the large paid sites would probably not appreciate that a smaller company was giving key features away for free. I would say this very comparable to Mint and Quicken. One is free and one is not, but offer similar services.

Long time ago, I used to have this belief "Oh! If I make a free software, I will have tons of users and then I can build a second product and market the second product to my audience from the first free software".

The problem is "You still need to market the Free product" and the effort is almost the same if you build a free or paid product. So why not build something useful and charge for it?

Just by building free tools or products does not drive traffic.
Just by building free website or service does not drive traffic.

You have to spend time and energy to bring traffic, free or paid does not matter.

Sometimes free makes it easier but only if it is useful and people want it badly.

The amount of effort required to market your Free or Paid service is almost same. If you have money to spend then you can delegate the effort but there is not much difference.

I would go with free during the initial phase (alpha,beta stage) but definitely go towards monetization eventually.