Friend, in general, edge detection is a highpass filter, those kernel based methods are performing spatial-highpass filtering, the main different between each method as you listed in the message is,
1. the filter coefficients; image spatial-frequency to pick up intensity variation for edge formation
2. the filter boundary discontinuity; ringing on sub-mage spatial-dimensional discontinuity during filtering (convolution)
For detail of each method comparision, I suggest you can search IEEE papers for further understanding.
Added after 15 minutes:
Oh, forgot this,
3. The spatial-dimension of kernal; a 3X3 and 5X5 kernal has different filtering results
Friend, except spatial domain edge detection, you may try frequency domain edge detection method, the Wavlets edge detection mathods I had used for my project like Haar and DB6 filters are very much effective that spatial filtering methods.
Yes, for sure with many papers had been proven Canny edge detection that captures points of sharp variation in an image by calculating the modulus of its gradient vector has algorithm complexity for implementation. By the way Canny operator is not a kernal based method.