Extensive studies have shown that the fractal scaling exists widely in real complex systems, and the fractal structure significantly affects the spreading dynamics on the networks. Although node influence in spreading dynamics of complex networks has attracted more and more attention, systematical studies about the node influence of fractal networks are still lacking. Based on the flower model, node influences of the fractal scale-free structures are studied in this paper. Firstly, the node influences of different fractal dimensions are compared. The results indicate that when the fractal dimension is very low, the discriminability of node influences almost does not vary with node degree, thus it is difficult to distinguish the influences of different nodes. With the increase of fractal dimension, it is easy to recognize the super-spreader from both the global and local viewpoints. In addition, the network noise is introduced by randomly rewiring the links of the original fractal networks, and the effect of network noise on the discriminability of node influence is analyzed. The results show that in fractal network with low dimension, it becomes easier to distinguish the influences of different nodes after adding network noises. In the fractal networks of infinite dimensions, the existence of network noises makes it possible to recognize the influences of medium nodes. However it is difficult to recognize the influences of central nodes from either the global or local perspective.