Karma yoga means doing the varnashrama dharma without expecting the results and dedicating the results to the antharyami.It has bhakthi underneath it.An example is king janak.

In Bhakthiyoga Krishna advises you to "Leave all your dharmas and surrender to me.I will save you"

Here you leave everything and have only him in your heart.This probably is the most painful of all paths.YOur family will call you a coward,your wife wont understand you.Swami dhukaram is an example.

Both karmayoga and bhakthi yoga need the same iron will to follow.Both need bhakthi.One cannot be said to be better over the other.One doesnt ask "which god is powerful,one in tirupathi or one in panderpur".