Both should work well "often enough".
I would trust the soldered version more, because the press fit version relies on a contact which in turn relies on proper case closure and fitting, and also on contact integrity.
In most cases the cases are clip together or screw together and contact pressure will be maintained well enough.
If I was building something using this style of battery and reliability was of utmost importance, I'd consdier having the battery case guide physically fixed to the PCB.
In some holders the battery slides sideways into the PCB mounted holder so that negative terminal contact pressure is maintained when the case is open.
In most cases this is not strictly essential as the positive terminal circumferential ring maintains enough grip to stop the negative terminal contact pressure reducing too much.
If designing from new, consider ensuring that the positive case contact cannot be "folded" by clumsy insertion so that it either malforms and reduces pressure or, worse, shorts out the battery.
I recently inserted batteries into a device which provided for two coin cells connected in parallel (a common arrangement in some products). The device started operating when the first battery was inserted. It stopped when I tried unsuccessfully to insert the second battery. It took a few moments for me to realise that the first battery was now being shorted by the bent positive contact on the second battery holder :-( .
It is worth looking at what known competent manufacturers do.
HP "they don't make no junk" - or they didn't used to 20+ years ago when the HP 10BII calculator was introduced.
Shown below is the battery compartment of an HP 10BII calculator. (I bought it in well used condition from an Op-shop for a $1 , earlier this year). It is not certain which method HP use here because they use a small extra piece of plastic to maintain the integrity of the battery box regardless of the state of the battery door.
In your example the case halves are clipped/screwed shut when the door is open - but that is true of the HP too, and they saw fit to design it so that the case closure state is unimportant.
As a general rule, doing what HP did in their designs before they split in 2015 is usually a good idea. After that date it varies.

Just to be sure that we made the best design choice, we were comparing the functional aspects of both these designs.
– Mandeesh Singh Aug 03 '23 at 11:17