Computerized sewing machines are normally considered to be more advanced than mechanical sewing machines. Mechanical sewing machines have good, solid basic features and are perfect for beginners, and those who want solid quality behind fewer features. In contrast, computerized sewing machines offer sewers greater variety and usually have more automated features.
For example, computerized machines often have a greater variety of stitch settings. Aside from just a basic straight stitch, you will also have a variety of different stitches for various shapes and sizes of zigzag stitches and more decorative stitch options. These stitches also tend to be able to be adjusted in more detail with more precise control over needle position, and over the length and width of the stitches.
If you are looking to buy a computerized sewing machine, you should also look at what automated features are available for that model. For example, some more advanced machines have automated controls to control the up / down position of the needle when you stop, or automatically sew a back tack when you finish sewing a seam. Some machines will be able to automatically back tack at the end of the seam and then trim the thread as well.