Image cartoonization is recently dominated by generative adversarial networks (GANs) from the perspective of unsupervised image-to-image translation, in which an inherent challenge is to precisely capture and sufficiently transfer characteristic cartoon styles (e.g., clear edges, smooth color shading, vivid colors, etc.). Existing advanced models try to enhance cartoonization effect by learning to promote edges adversarially, introducing style transfer loss, or learning to align style from multiple representation space. This paper demonstrates that more distinct and vivid cartoonization effect could be easily achieved with only basic adversarial loss. Observing that cartoon style is more evident in cartoon-texture-salient local image regions, we build a region-level adversarial learning branch in parallel with the normal image-level one, which constrains adversarial learning on cartoon-texture-salient local patches for better perceiving and transferring cartoon texture features. To this end, a novel cartoon-texture-saliency-sampler (CTSS) module is proposed to adaptively sample cartoon-texture-salient patches from training data. We present that such texture saliency adaptive attention is of significant importance in facilitating and enhancing cartoon stylization, which is a key missing ingredient of related methods. The superiority of our model in promoting cartoonization effect, especially for high-resolution input images, are fully demonstrated with extensive experiments.