I'm operating under the assumption that you're using the magazine billing model -- sign up today and you will be billed in 30 days unless you cancel in the interim. This is opposed to the shareware billing model -- sign up today and you will not be billed until you make an affirmative decision to purchase.
The magazine model has a lot of funnel dropout at the first stage (sign up) and fairly little dropout at the second stage (cancellation). The shareware model has less drop out at the first stage (sign up) and hideous dropout at the second stage (decision to pay).
For a service, I'd go for the magazine model. (A lot of non-technical customers assume you're going with the magazine model even if you're not. I get an email on a weekly basis asking to cancel a downloadable free trial.)
One possible exception is if you think your free trial is likely to be in-freaking-sanely sticky for users that start with it. In that case, you might want to make up the difference in conversion rates in sheer volume. Another possible exception is if you get business value from free trial users. For example, if your software has strong network effects, or if you are running an online game and free players are essentially bonus content for playing players, then you might want to encourage as many signups as possible even if you knew a-priori that you would fail to monetize most of them.
Note that if you collect information prior to collecting authorization you've got some headaches to think about beyond the scopes of conversion rates -- information security, whether your payment processor will let you do it, etc.