Bump-feed string trimmers utilise a spring underneath the spool. When you tap or bump the head against the ground more line comes out. Automatic-feed string trimmers utilise an automatic-feeding system that pushes more line out whenever it gets too short. These different line-feeding systems have their own positives and drawbacks and, depending on your needs, will fit a wide array of trimming necessities.
The bump-feed system offers the user the freedom to get more to cut with whenever he wants, which can be done on the fly. The automatic-feeding system draws out more line only when it reaches a certain shortness. While the bump feeder is quicker, it also uses up a lot more line, which can add up in the cost department, and the time needed to replace the line. The automatic-feeding system allows you to keep trimming while the line feeds itself out, so you will probably end up using less line. Consider for how long you need to use the trimmer and how large the job is. If you need lots of line, then the bump-feed system will offer the best advantages. If you have a smaller line and don't like hassling with replacing the line every time you use the trimmer, consider the automatic-feeding system.
The automatic-feeding trimmers generally use replaceable pre-wound spools. Bump-feed systems allow you to remove the spool and rewind the line whenever it runs out. Pre-wound spools are more expensive than a bulk roll of line, but the time needed to rewind the spool each use may deter you from purchasing a bump-feeding trimmer. Again, if you need lots of line, you'll probably want to use the bump-feeding trimmer, but if your lawn is small and your short on time, you'll probably want the automatic feeder.
Each system comes with its own set of maintenance issues. The bump feeder uses a spring, which can fly out unexpectedly and injure you or people nearby. This spring can also get worn out if you've bumped it too much, so line won't come out properly until a new spring is installed. The pressure from bumping can also crack the spool inside the head. The automatic feeder uses a motor inside the head to unfurl more line. This motor can become damaged or break over time. Trying to repair this motor and parts by yourself may be difficult and more expensive.
Upfront the bump-feeding trimmers generally cost more, but with less maintenance and a longer life, they may represent a savings over the long run. Automatic-feeding trimmers take a lot less line, but you typically need to replace the entire spool to replace the line. In the end, the costs are quite similar and it really comes down to personal preference and what your usage level of the trimmer will be.