As technology becomes more advanced, unfortunately it also means that machines can become outdated.
While fundamentally the surgeon plays the most important role in deciding which treatment option works best for the eye and the patient, scientifically speaking, the machine does make a difference.
Case in point: a research paper I co-authored years ago, based on very careful studies on real life patients in Singapore published in 2012 in a peer-reviewed scientific journal:
The study found that the Wavelight is better in predictability.
There are numerous other similar studies comparing other different LASIK lasers and the results that are published in respectable journals are usually referred to by doctors in the know.
Unfortunately it can get real confusing for the lay person with so many different lasers around.
In fact, the few laser names you quoted are in two groups: the first two are the femtolasers to create the LASIK flaps, and the last two are the excimer lasers to sculpt and change the focusing power of the cornea, all of which I am quite privileged to be familiar with and have used before.
There certainly are some subtle differences between them.
I would suggest if you find it interesting, take your time finding out more about the different lasers, and consulting a trusted, knowledgeable surgeon who may be able to explain more about his or her choice of recommended lasers versus others. After all, LASIK is an elective surgery, and as a patient, you do have a right to know.
Cheerio and all the best!