There are a multitude of things to consider.
One primary one is, what is the shape of the pins you plan to insert into the socket ?
Thin flat pins, characteristic of IC's, are better off in a dual wipe socket than an round machine pin one.
However, if you have items such as IC adapters, with round Gold pins in the diameter range of 0.45 to 0.55mm, these are not good in a dual wipe socket and are excellent in a machine pin socket.
Then there is the issue of repair-ability.
One great advantage of the modern dual wipe socket is, that if one of its claw structures gets damaged, you do not have to replace the whole socket. You can withdraw one claw arrangement at a time from the top, and replace it if you wish.
On the other hand, you cannot do that with a machine pin socket, because of the way is pins are molded into the plastic. And the plastic of the machine pin socket is too brittle to cut, without bending the pins and risking track and pad damage to do a one pin at a time extraction.
In addition, the cross sectional area of the machine pin socket pin, can be a significant proportion of the hole size in the pcb, making solder sucking more difficult, not always, but sometimes, depending on the hole size , and as noted the shoulder on the machine pin socket, even after solder sucking, can stick to the pad around the pcb hole, risking lifting off pads/tracks when the socket is removed.
So, on all the factors, checks and balances, the "safer" option is the dual wipe socket especially for flat pin device projecting into them. This provides the better option for future repairs too. But, still I go for round pin socket if the pins I'm putting into them are round in cross section and no bigger than 0.45 to 0.55mm in diameter.
And still there is something else:
Any of the comparisons between the merits of both styles of the socket designs are pointless, if the sockets are poor quality cheap knock offs. Often this is because the Metallurgy is not ideal and the material not springy enough. So after a few insertions and removals of different IC's the claw tension is lost and the spacing between the claws permanently stretched because they don't go back to their original geometry after being opened up a few times by whatever was put in the socket.
This is why you should never put any object into an IC socket (that is normally receiving an IC pin of about 0.3mm in thickness), like some adapters, that is bigger than about 0.45mm diameter, because it will stretch the claws apart, permanently, especially in cheap sockets, then making it unreliable for an IC put back in the socket later. But, oddly there are many adapters for "this and that" out there with very fat pins, that damage IC sockets, even good quality ones, from the perspective of putting an IC back into them later.
Of course it would be fair to say, if you only ever put an IC into a socket once, never had to remove it, and never had to replace the socket, then the difference between the two types of sockets diminishes to near zero, and in that case I would use the machine pin type. And taking that further, if the pcb is single sided, without plated through holes, I would use the machine pin type too, because they are effortless to un-solder in that case.
