These are strictly professional cars. When they are not "in duty" they're probably parked at a garage.
On the other hand, an American open truck driving/parked in a residential area is almost certainly some show-off.
Source: I live here and see it every day. Family, friends and customers are doing it, plus many eons ago I too was a tradesman driving home every day in the company work van.
(Heck, many companies wouldn't even have a place to park all their company cars at once, many such smaller companies run out of regular residential buildings with no dedicated parking.)
Seems correct on relative length but not width; the F-450 Super Duty body is a bit wider without mirrors than a Sprinter with mirrors;
A standard mercedes sprinter in van configuration is 2020 mm wide without mirrors, which is as wide as the RAM and just 10mm narrower than the f150. I suspect the sprinter has wider mirrors, but I don't have the F-150 numbers to compare to so I'll leave that unanswered. Pickup configurations of the sprinter go much wider (and have extended mirrors to fit) - a common compact pickup bed configuration has a 2030mm internal bed width for example.
Note that the F-450 Super Duty is not applicable to the discussion as it won't work in the EU: A standard vehicle (class B) has an upper weight limit of 3500 kg. The F-450 Super Duty would have to be registered as an actual truck (class C), which requires a different drivers license and the use of a tachograph to track all driving and adherence to resting period rules. We don't use those vehicle classes unless strictly necessary.
It's the norm in many businesses for employees to drive their work vehicle home and park it where they live, so they're everywhere. Not as many as regular passenger cars of course, but you'll see them on any residential road. Gardeners, plumbers, electricians, delivery services, this is the norm for all of them (a perk of sorts). Even big name-brand logistics companies, as it's common for the drivers to be independent contractors owning the van themselves so home is the only place to park.
They are also used for errands. They're legal for private use proportionate to the amount of VAT paid irrespective of registration type here, so you'll see them pick up/drop off kids, do groceries, recycle bottles, etc. in such vehicles too. Pretty sure that would be just as legal where you are given familiar EU rules.
As I said, I rarely see Sprinters, might be an Amsterdam thing due to how hard it is to drive and park them here. Ford Transit / VW Transporter / MB Vito / Renault Trafic are far more common. It doesn't seem like much, but an extra 20cm width + 1m length make a massive difference in overall size and driveability.
For example, a Mercedes Sprinter in the standard long box configuration (as is used by local grocery delivery services, plumbers and the likes where I live) is 7.4 meters long , way longer than even the longest American pickup trucks (for some of them, several meters longer!), and is just as wide as them.
In custom box or pickup bed configuration (used by e.g., gardeners), these vehicles get wider (and sharper).