The Sick Need Doctors

You're right that this involves prudential judgment, which ultimately rests with each person discerning how God is calling them to use their resources. But the Church does offer principles that can illuminate the question.

Scripture presents both duties as essential. Christ commands us to "make disciples of all nations" (Matthew 28:19), while also teaching that care for "the least of these" among the brethren is care for Him (Matthew 25:40). The early Church held these together—evangelization and mutual aid weren't competitors but expressions of the same love.

The Catechism teaches that charity "is the soul of the holiness to which all are called" and must extend to all, though it also recognizes a certain "order of charity" rooted in proximity and relationship (CCC §826, §2197). St. Thomas Aquinas, drawing on this tradition, noted we have special obligations to those bound to us—family, community, fellow believers—without diminishing our universal call to love.

Practically, the Church has never taught that preserving Christian lives and evangelizing non-believers are mutually exclusive. Often they reinforce each other: Christians sustained through persecution become witnesses; new believers strengthen the Body. As Evangelii Nuntiandi §41 notes, the witness of life itself is the first form of evangelization.

The discernment is yours to make in prayer. But the tradition suggests you needn't choose between loving your brothers and loving those who don't yet know Christ—both flow from the same source.