System.Web.Mail is not a full .NET native implementation of the SMTP protocol. Instead, it uses the pre-existing COM functionality in CDONTS. System.Net.Mail, in contrast, is a fully managed implementation of an SMTP client.
I've had far fewer problems with System.Net.Mail as it avoids COM hell.
The few times I ran into this, I found that that the methods and properties were all almost identical- changing the object type was just about all I had to do. There were one or two other little things, but they showed up with the lines and it was obvious what to do with Intellisense. I'd vote for going with the fully managed solution, get away from cdonts as soon as possible. It's not even installed on 03 server and newer.
System.Web.Mail is deprecated, but should still work. You'll be annoyed with warnings about it being obsolete, but the functionality still carries on... for the time being.
I would agree with others that the conversion to System.Net.Mail was very trivial. I doubt you'd have to re-write more than a line or two.
Biggest issue with System.Net.Mail is that it has no support for Implicit SSL. Use System.Web.Mail until you don't have a need for Implicit SSL support.