Merriam-Webster's online dictionary defines proselytize as:
1.) to induce someone to convert to one's faith
2.) to recruit someone to join one's party, institution, or cause
It defines evangelize as:
1.) to try to convert (a group or area) to a different religion (especially Christianity)
2.) to preach the gospel to
3.) to convert to Christianity
As I interpret it, from these and other definitions not presented as redundant, evangelize denotes an attempt to effect a conversion of multiple individuals to Christianity, specifically through preaching the Gospel. Proselytize (again, my interpretation) means to use persuasion or influence to motivate single individuals to regard a certain belief or set of beliefs--which may or may not constitute a religious faith--as true and worthy of adopting.
In context:
We just visited every home in the city. That's the way the church in
Jerusalem first evangelized that city. The disciples there evangelized
the entire city of Jerusalem in a very short time. All the other
churches in Asia Minor have followed that example.
--Gene Edwards, in an imaginary interview with 1st Century evangelist Aquila of Ephesus in How To Have A Soul Winning Church p. 28.
Gospel Publishing House, Springfield, Missouri. Pub. date unk.
Merriam-webster online, wordnik.com, dictionary.com, the Cambridge Academic Content Dictionary and wiktionary.org all describe proselytize as an action directed at a single individual (or collective equivalent, i.e. "everyone"). I could find no definition wherein proselytize took a distinct assemblage or a plural number of discrete persons as its object, nor could I locate any contextual usage using that framework.
And now, for the actual answer to your question, I offer (with a caveat) the following construction:
"A proselyte wants to persuade the inhabitants of a city to convert to his faith; an evangelist has the faith to persuade an entire city it wants to convert"
The caveat: Understand that evangelize is appropriate only if referring to promulgating Christianity, and would be a poor choice in another context.