Here are some pros and cons off the top of my head.
Standard button.
Pros - No mechanical lock to fail.
Cons - Generally, seems to be the least secure method. Straps can more easily slip off a standard button. The button hole in the strap gets more pliant and less secure over time depending on the material used. Some straps apparently come with strings and other methods for making the connection to the button more secure.
Dunlop recessed strap locks.
Pros - Visually appealing. For a collector instrument that's not played often, the recessed locks do not detract from the visual lines of the body the way strap buttons do.
Cons - From what I've read here in the forum, there seem to be a greater number of reports of mechanical failures of the locking mechanism than with Schallers; and given the numbers of Dunlops and Schallers, the Dunlops seem to fail at a far greater rate. Installing recessed locks on an existing instrument is not the simple operation that replacing a standard button with a Schaller button is. If you have several instruments, unless they all happen to have recessed locks, you will not be able to use the same strap on all of them.
Schaller strap locks.
Pros - The button is an easy replacement of the standard button; thus putting them on all your instruments is an easy task. And if you want to put the original button back on when you sell the instrument, it's not a problem. The connection between the lock and the button feels secure; it seems to be a much more secure connection that a standard button.
Cons - There have been some reports of failures; though it seems that, as a percentage, the number of failures is small. This seems to be by far the most popular method. The nut holding the lock to the strap tends to get loose and needs to be tightened immediately when it does. (I've been meaning to try some small lock washers, but haven't yet.) The threaded section, over which the strap's button hole is placed and secured with the nut, seems generally to not be long enough (which means there may not be room for lock washers).
Direct connection.
Pros - Screwing the strap directly to the body is the most secure method. There are no mechanical locks to fail.
Cons ? When you are ready to play, or when finished, you have to raise the instrument up and slip the strap over your head. Obviously, if your playing position has the instrument at your chest, it's more of a problem than if your playing position is at your belt; you have to raise the instrument higher and the available room to slip your head through the strap is less. This can really be a problem when playing on a stage with a low ceiling. (I used to play a lot at a popular blues venue where the ceiling was only a few inches above my head.) Also, if your case is form fitted for your instrument, having a permanently attached strap may be a bit of a problem.
There are some other methods as well; and there are more pros and cons. But this is all I can come up with at the moment off the top of my head.
Personally, I use Schallers on all my basses and straps. I?ve never had a lock failure. The nuts do get loose from time to time; and that is worrisome. I always take the strap off before putting the bass in the guitar stand. (I can?t remember why I started doing that, but it does seem safer.) (I also always remove the cable before removing the strap and never put the bass in the stand with the cable still attached.) And I also don?t put the strap in the case with the bass. And when I put the strap on, I always check that both buttons are locked into place. My playing position is fairly high up on my chest; thus my strap length if fairly short. I don?t think I would feel comfortable having to raise the bass up and slip my head through the strap every time I pick up or put down the bass. For me, it seems the chances of hitting something with the headstock, like a par can hanging from the ceiling, are greater than the chances of a lock failure.
But that?s just me. Other members? preferences can be as reasonable for their situations as mine seems to be for my situation.