The questions that I think you want to address first are
"What do you want the user to do?" and "What does the user expect?"
Do you have different markets for the two versions of the apps? Are you pushing some users towards one app and others to the second? Is there an upgrade path?
How does the functionality differ? Why would somebody want the "extra" functionality if there is any? Can you get those users to self-identify by the naming?
To pick an example from our domain. We don't have "OmniGraffle" and "OmniGraffle Plus" - we have "OmniGraffle" and "OmniGraffle Professional". Notice how using a more role based name automatically sets some expectations on the kind of user who'll be using that version.
Or look at the way the pricing bands on bid sketch are named. The "Freelancer", "Studio" and "Agency" labels immediately give major cues as to what levels of functionality the different bands expose.
Suffixes like "Lite" and "Free" only reveal that there are functionality and cost differences. The user then has to go dig out the implications. Are there ways that you can help them do that via the naming.