Sorry for the off-topic, but which is better, 3ware or LSI Logic ?
This varies. It will depend on specific needs, as well as if you're looking at SAS/SCSI or SATAI/II, and how many ports. Generally they're fairly interchangeable, though both manufacturers put out some cards that are superior to their counterpart. In short, check the benchmarks on the specific card before you buy. Also, add adaptec to your list.