To conclude about what's better between AES 256 vs 128, we should be aware that AES comes with three standard key sizes (128, 192 and 256 bits). Many people see this and think that if there are three distinct sizes instead of just one, then there must be some difference, and since the 256-bit version is a bit slower than the 128-bit version (by about 40%), it must be "more secure". So they go for "the most secure" and choose 256-bit keys.
In reality, the AES has three distinct key sizes because it has been chosen as a US federal algorithm apt at being used in various areas under the control of the US federal government, and that includes the US Army. The US Army has a long-standing Tradition of using cryptography, and that Tradition crystallized into internal regulation with all the flexibility and subtlety that armies around the world constantly demonstrate (just listen to some "military music" and you'll understand what I mean). Unfortunately, this happened quite some time ago, before the invention of the computer, and at that time most encryption systems could be broken, and the more robust ones were also very hard and slow to use. So the fine military brains came up with the idea that there should be three "security levels", so that the most important secrets were encrypted with the heavy methods that they deserved, but the data of lower tactical value could be encrypted with more practical, if weaker, algorithms.
These regulations thus called for three distinct levels. Their designers just assumed that the lower level were necessarily weak in some way, but weakness was not mandatory. So the NIST decided to formally follow the regulations (ask for three key sizes) but to also do the smart thing (the lowest level had to be unbreakable with foreseeable technology). 128 bits are quite sufficient for security (see this answer for details). Therefore AES accepts 256-bit keys because of bureaucratic lassitude: it was easier to demand something slightly nonsensical (a key size overkill) than to amend military regulations.
Most people don't know or don't care about History, and they just go for it because they feel they deserve it.
