I have a number of vises of various types not to be confused with my vices of various types. I've found most screwless vises to be more than adequate, more compact for their size, and cheaper than a mill vise. Lockdown or otherwise. Some may argue they are not as easy to use, but in my CNC enclosures I can't spin a handle anyway. Its actually easier to loosen the jaw and slide it to the next notch than it is to swing a handle on a mill vise. Being more compact may not be an issue for some, but I have enclosures for a reason. I sure don't want to knock the window out of my enclodure doors by slamming a vise into them. I have three small (6.5 x 11.5) high speed cnc mills with screwless vises on the table that allow me to cut my maximum size part (6x11). I admit I did machine the jaws to optimize everything, but they get used every single day. They hold very securely and if there is any jaw rise its minimal. From .0005 - .001, although to be honest I have not really noticed. I use a high hold in the top 1/8 of the jaw so if there was going to be an issue I expect I would notice.
I have nothing against milling vises. I have a bunch of them. 8 or 9 atleast. I only have two of them in service on the table of my largest mill (14x24) though. I do use them everyday, but I designed the enclosure on the table to be big enough for them. Still its a pain to spin and swing the handles for long jaw travels so I use an air wrench for long moves and then use the handles to tighten and loosen on the stock. I used a pair of screwless vises on it for a long time too, and sometimes I consider going back to them, but that brings us to the one (in my opinion) big drawback to a screwless vise. Unless you are prepared to mill, drill and tap them they are limited to their design size. A mill vise can easily (the ones I have anyway) have jaws moved or machined for the opposite side of the jaws to as much as double their capacity. None of the screwless vises I have were designed with that in mind. I might note I bought some vises from a shop that closed down and I have not confirmed all of those can have jaws on either sides of both parts of the closure. I did have a very cheap mill vise that was inside jaw only, but I let it go with a mill I sold in the last year.
In conclusion I feel for an occasional or hobby user or for a user that does not need to spin the vise on a swivel base a screwless vise can be a very good low cost alternative.
Note 1: Before buying a screwless vise with intent to modify it bare in mind that they tend to be pretty hard steel. They will tear up tooling.
Note 2: I have not seen a screwless vise that comes with a key on the bottom to align with the table t-slots. I do not use keys anyway. I line up my vise or vises, rough clamp them in place, and dial them in with a test indicator. If the jaws are decent its not that hard to get them within .0005 over the length of the jaws. Some guys can do better I am sure.