In this paper, we carry out a performance analysis from a probabilistic perspective to introduce the EDHVW methods' expected performances and limitations. Then, we propose a new general error diffusion based halftone visual watermarking (EDHVW) method, Content aware Double-sided Embedding Error Diffusion (CaDEED), via considering the expected watermark decoding performance with specific content of the cover images and watermark, different noise tolerance abilities of various cover image content and the different importance levels of every pixel (when being perceived) in the secret pattern (watermark). To demonstrate the effectiveness of CaDEED, we propose CaDEED with expectation constraint (CaDEED-EC) and CaDEED-NVF&IF (CaDEED-N&I). Specifically, we build CaDEED-EC by only considering the expected performances of specific cover images and watermark. By adopting the noise visibility function (NVF) and proposing the importance factor (IF) to assign weights to every embedding location and watermark pixel, respectively, we build the specific method CaDEED-N&I. In the experiments, we select the optimal parameters for NVF and IF via extensive experiments. In both the numerical and visual comparisons, the experimental results demonstrate the superiority of our proposed work.