CHRISTIAN OR NOT?

This past week brought about a question that touches on the question of "How can unbelievers look at times more like Christians, than Christians themselves are supposed to act?" Meaning, there are many Christians who do not behave as Christians ought, and yet there are unbelievers who behave more like Christians in their good works. I hadn't really contemplated this much recently, although it has crossed my mind several times in my life, but a comment was made out of the blue that again caused some thought. The comment is presented below. I throw it out there, more as thought provoking material, and wonder what some of you might think of it, not because I am seeking answers, rather, just to see what others have to say.

COMMENT:
"We can do good works on our own, but we can't do eternal work on our own. We need a power greater than ourselves to do eternal work."
A study in Colossians 1 is where this comment arises.

I ask you, would this provide an answer to those who claim that even unbelievers can do good works? Besides the motivation, is there a difference between an unbeliever's good works and a believers? Can unbelievers do good works? If so what kind of good works are accomplished? Works such as offering financial assistance to those in need, working to relieve hunger around the world, helping in rebuilding disaster areas, are these good works even by unbelievers? Visiting older parents in a retirement center, providing for one's family, taking a meal to a sick neighbor, are these good works? Even some unbelievers would claim that these good works were not selfishly motivated. Would you look them in the eye and tell them that they were wrong and that their good works did not count for anything because they were selfish just from the fact that they are an unbeliever? Do not Christians perform good works out of selfish motivations? If so, does this differ with the good works unbelievers do? How would you explain the difference between an unbeliever's good works with that of a believer's? Does the above comment offer any explanation?

Again, I don't pose these questions because I am in a personal struggle in the matter. It's a topic for conversation and something to challenge every person's thinking. Call it table conversation. What do you think?