I really dislike calipers with those thumb wheels.
They mess up with the feeling of the force I use to adjust them.
It also makes it harder to open the calipers, as the travel distance is only half of what your thumb does.
The thumb wheel does have the (at least theoretical) advantage of a finer adjustment.
Another disadvantage is that it's only on one side. I've ground the back corner (opposite to the side of the ribbed thumb support) of my Mitutoyo's because I used them in weird angles too many times and the only way to exert a measurement force in those positions was on the back side.
In the end though, it's mostly what your're used to I guess.
Having both variants, and taking turns using them is the most nuisance though, as you have to adjust the measurement force for reliable measurements.
The adjustment with the screw can be useful in some situations, depending on what you use your calipers for. You often see them on height gauges, and I have a 500mm calipers with it, but have not used it much.
Most important though is to avoid the cheap garbage.
I have 3 mitutoyo's and I've had 2 of these for 30+ years and they're still good. Mostly have slight scratches on the backside.
I've bought a bunch of the cheap digital ones, and they all ended up in the garbage. A few years back I bought a digital Mitotoyo CD-15APX and it just keeps on going on its first battery.
I can sorta understand if you don't want to sink EUR100 or more into a set of calipers (even when they last 30 years, that's EUR 3 per year!). But still. Avoid the EUR15 cheapies. There are some decent quality chinese calipers for around EUR 30 to EUR40.