At a basic level, which for a Buddhist means you're striving to live morally pure life, cultivating love and compassion and learning how to avoid hurting others, the difference is not very important, since they teach the same ethical message, about compassion, altruism, loving-kindness, humility, and so on. The main differences at that level are:
1. They both agree on what a morally pure life would be (being kind, loving, compassionate, generous; avoiding killing or harming others, lies, stealing, and so on), with the main difference that Christians mainly include human beings while Buddhist try to cultivate the same attitudes and actions toward all living beings.
2. One obvious difference is, however, that Christianity merely endorses those qualities, while Buddhism is more like a practical toolbox that actually teaches effective methods on HOW to develop those desired qualities, like how to decrease hate, anger, miserliness, pride, egotism, and instead increase love, compassion, generosity, patience, tolerance, humility, and so on.
3. Another obvious difference is that Christianity teaches that you actually can't fully develop those qualities (by your own power), and that you in the long run can't liberate yourself, whereas Buddhism on the contrary teaches that only you yourself can change yourself and liberate yourself, that you and everyone else really have the capacity to do so, and that there is no use in trying to look for help from the outside.
Taken together, this means you can be a fully faithful Christian and still use the methods (but not all of the beliefs) in Buddhism. From a Buddhist perspective that's no problem at that level - as long as your Christian beliefs help you develop the love, faith, harmony and good qualities you need, it is nothing but a good thing. From a Christian perspective there can be no fault whatsoever in applying effective methods for developing morally good qualities, so the combination is not only possible, but often a strong one.
A few more principal differences are these:
1. The Buddha said there is true hope for everyone. We all have the Buddha-nature, i e the ability to reach enlightenment. In the end, everyone will become a Buddha. No eternal hell and condemnation. The main difference is that hell (and heaven) in Christianity is eternal, whereas in Buddhism it is only temporary. After some time in a hell (or in a heaven), you will be reborn again and continue your way towards final liberation and buddhahood.
2. The Buddha's teachings are possible to try out in order to see if they are good or not. On the contrary, Jesus' teachings are to a great extent a revelation from a source that you can never prove or disprove - just a matter of belief.
When you have travelled far on the Buddhist way and have reached the levels where you want to strive for liberation from Samsara, for wisdom and for full buddhahood for the sake of liberating all living beings from suffering, then there are more contradictions that more clearly show they are based on fundamentally different philosophical worldviews. Just to name a few:
1. You can't, when you delve deeply into the philosophies, combine the Buddhist teachings of emptiness and selflessness with the Christian beliefs in an eternal creator God, an eternal soul and the belief in absolute truths.
2. You can't at the same time say you rely only on God for your salvation and say no one but yourself can do the work.
3. The Christian views of sin and punishment, good and evil, creation from nothing, time, eternity, faith in a higher being, revelation, commandments, and so on, are very difficult to harmonize with a Buddhist worldview (you can reinterpret them in a Buddhist way, but the question is if you're then still a Christian).
To be more specific on the question you asked about judgment and karma: On the practical level I agree the effect is quite much the same, in that you do good things because they lead to good results for yourself and others, and you avoid bad things because they will lead to bad results. On the theoretical level, however, the difference is very big: the Christian judgment is executed by an outside power (God), who evaluates your life and deeds, gives his sentence, and executes the eternal punishment or eternal reward; whereas the theory of karma is nothing but a way of describing (and theorizing over) the law of cause and effect, totally without any judge or executor. See more in my answers to these questions:
Nevertheless, it's fully possible (and increasingly common) to be for instance a Christian and at the same time draw meaningful inspiration from Buddhist thinking and Buddhist methods. See more in my answer to this question:
Buddhist, ex-Christian. Studied Christianity and Buddhism both at university and through religious institutions.