As you know, "Mom Bikes" (mamachari, ママチャリ) are huge in Japan. It's not unusual to find some with three sets of child seats (in front of handlebars, behind handlebars, and behind seat). Many contemporary mamachari now are electric assist, which is great. Note that even when a dad rides a mom bike, it's still called a mom bike.
A quick sidenote: child trailers which are very common in the USA and
front-cargo bikes such as are common in Denmark, are not common in urban parts of
Japan. They are simply too long to park in most supermarket and train
station bike stands. The only trailers I've seen in Japan are ridden
by foreigners. The only front-cargo bikes are for delivery companies.
You should check where you expect to park the bike to see if there's space.
This is less of an issue if you're in the boonies.
About buying and attaching child seats to mom bikes:
Rear Seat: The child-seat that sits behind the main seat is a standard design that is designed to be easily attached (and then detached when the kid gets larger). You can get these types of seats on the after market and they'll be just as good as getting them pre-installed on a new bike, assuming your old bike has the proper rear-rack installed. Your bike shop will tell you when installing the seat about compatibility.
In your specific case, however, the bike with the rear seat pre-installed has smaller tires and an elongated wheelbase which aids in comfort
and safety (the child is lower to the ground and there is more space
between the child and the rider).
Mid Seat: The child-seats that are either immediately behind the handlebars can be found in the aftermarket. But as the bottom left image in the google-image-search above, you can see that some seat designs will cause knee-strike. Generally these should be avoided unless it's for a very small child or your bike is on the larger side and there's no risk of knee strike.
Front Seat: The bike seats that are placed in front of or on top of the handlebars are usually custom to that bicycle as they depend on the shape of the handlebars or front wheel.
Note also that mom bikes are very cheap on the used market (once kid goes
to school and mom goes back to work, the bike gets retired). So it may be cheaper to sell your bike and get a mom bike with a rack installed.
tl;dr: You can get a rear seat fairly easily and it should just plug-and-play on any standard mom bike that has a rear rack. Try to avoid trailers and cargobikes unless you know you can park them where you need to go. Explore used options. However, with the two bikes you've shown, the actual bike base is different (26" vs. 20" wheels, elongated wheelbase) so you might find the bike with the rack preinstalled more comfortable and safer for child and parent.