If you're having troubles with your guitar holding tune, make sure it's not issues with the nut or the method of tuning first otherwise you're just wasting money on upgrades. The tuners likely are pretty decent on those guitars to begin with, so I can't see upgraded tuners being a huge leap in tuning stability. Unless the tuner is broken or there's or theres a lot of lag in the gear teeth the originals should be fine. That said I'm a big fan of Gotoh's hardware. Topnotch and precise quality
No name tuners on every guitar seem good these days.
Locking tuners for me just eliminate a bunch of time, being careful with the windings, and stretching strings.
In the end the tuning stability is about the same.
Gotoh, fender, Grover on my guitars.
I find it comes down to precision, weight and build. As long as the tuner is functioning properly, there will be no real difference in terms of staying in tune. They'll all do the job.
Now some aftermarket offerings are more precisely made, specifically when it comes to gear lash. That's where the shaft and tuning peg gear mesh together. The more precise the interface is, the more precise the tuner is and there's no slack or free play when turning the pegs. So it's a feel/tuning to pitch thing rather than staying "in" tune.
And then there's weight if that matters one way or the other. I'm guessing most of the tuners on your guitar were made in China. I recently took off a pair of very well-made non-locking tuners on an import instrument and put Hipshots on there. Strange thing was, I swear the ones I took off are like a Chinese licensed Hipshot product. They were really solid. Strangely enough, the new Hipshots did not bolt/screw right in and needed the included adapter. Something to consider. But generally, the high end Gotohs, Hipshot and Schaller tuners are going to be better made products.
Some might have other features like cutting the string when locking the tuners down.
I've had a wide range of locking tuners over the years from all the big names and I mostly prefer the Hipshots at this point due to just about zero gear lash and the wide range of button choices they have. I use Gotoh lockers on two other guitars that are more "vintage". All work as advertised and are easy to use. I also used Gotoh on all of my Ibanez because they bolt right on and their hardware colors match.
The biggest difference between cheap tuners and good tuners isn't whether or not they hold in tune. Even cheap tuners will hold the string in place once it's there and the slack is out (tune up). Try putting a vice-grip on the tuning post and turn it.... it will break before it budges. The advantage of good tuners is that it is much easier and quicker to get it into tune because they are smooth and more precise. And for that, the best I've come across are the Graphtech Ratio tuners. My first reaction to them was, ...well that's cool, but it seems like a solution looking for a problem. But I put a set on my main strat and on my main acoustic, and they are a game changer. Not only are they among the best feeling tuners I've used, but the ratio feature makes them very intuitive to use. Every string reacts exactly the same to turns of the button... one complete turn equals a full step. If you do a lot of alternative tunings, these are a must! You can literally tune on the fly without even listening to the note. They're not cheap... about $100, a bit higher for locking, but if you are going through the expense and trouble to upgrade your tuners, these are the way to go.
I have guitars with Grover, Gotoh and now I just got a Cort with what look like generic Kluson style tuning machines. All hold tune just fine. Just like guitar pickups there really are not many bad tuning machines nowadays on guitars. The Grover mini locking machines are in my opinion the easiest to use (and most solid) because they lock and unlock by inserting a flat head screwdriver or edge of a quarter.
I only have experience of the vintage Kluson-style Gotoh Magnum without the thumbwheel, but I would definitely use them again if I needed them. The adjustable height posts are great for getting the perfect break angle across the nut.