I brought my Bianchi to the shop a couple days ago to replace the rear wheel. They ended up replacing both the hub and the wheel.

Here's the new rear hub they put on: https://i.imgur.com/16MATL0.jpg

And here's my front hub, which matches the previous rear hub: https://i.imgur.com/lS4rHie.jpg

It feels like the new rear hub has a lot more resistance. Should I ask for my old hub back? Is it possible to replace the wheel but keep the hub?

I don't know what the problem was with the old wheel, but the hub is integral to the wheel. The wheel consists of a rim, attached to a hub by spokes. It's all one piece.

As for the difference in resistance, it might be that the gearing is different if they changed the sprocket cassette, or it could be that there's some break in period for the new hub.

OTOH, the biggest noticeable difference in resistance (in the same gear) comes from changes in tires and/or tire pressure. Your problem could simply be lower tire pressure. Or, and don't be offended, it could just be your imagination (this is common).

I suggest you go back to the shop, and have them confirm that the hub (and wheel) is OK, so you can enjoy some piece of mind. Going back is important because there might actually e somethig wrong that needs to be adjusted out.

how do you judge the difference?

you take the wheel out, or this just effort from the pedaling?

I'd definitely ask for the rear hub back. I'd imagine it's still a complete wheel in their shop somewhere. Call them immediately.

Was the rim that needed replacing? Perhaps they didn't want to lace up a new rim, so just swapped out the wheel. Wheel swap was likely far cheaper than lacing up a new rim so if you expressed any cost sensitivity they might have sensed that was out of your budget.

If it was cogs that needed replacing maybe they didn't have any freewheels on hand so went with new wheel and cassette.

same old hub in a custom, hand built wheel is certainly possible , if you are willing to Fund the work.

When OP says wheel, I think he means just the rim. Hence saying he got a new "wheel" and hub, e.g. a new rim and hub (and incidentally spokes).

While it's not really going to affect your 'speed', you had an old Campy hub, they always tended to frrl very smooth, the 'new' hub is a probably a generic hub, it'll be fine, but I would try & get that hub back.

Campagnolo?
well definitely get the old hub , unscrew the freewheel before taking the damaged rim off, please ,
or the hub would be unusable.. you need the leverage of the rim to unscrew freewheels.

Factory wheels, particularly of the budget variety, often come with poorly adjusted bearings. And hubs with cartridge bearings will often show noticeable seal drag. While this rarely causes any huge differences while riding, it's generally easily noticed when spinning the wheel.
Tight bearings should be adjusted ASAP, and dragging seals will fix themselves with time.

They replaced the entire wheel. To remove your old hub and rebuild it into a new wheel would have cost more than $200 in parts and labor. And the hub and freewheel may have needed replacing anyway. It is not possible from your description to tell if the main problem was one or more of the following:

• Worn out braking surface on old rim
• Impact damage on rim
• Worn out or damaged freewheel
• Worn out balls or cones on old hub
• Broken or seriously damaged spokes
• Etc.

In any case, the shop did what they should have done with a 30 year old wheel. But make sure you get your old wheel back. Looks like a nice old Campy Chorus or Victory hub. If it was up to me on my spare time, I would have replaced the freewheel and laced in a new rim with the existing spokes (the rim is likely the key problem), regreased the hub, and had myself a very nice wheel.

No point the shop guys selling this to some collector for beer money when you could do the same.

If by this you mean the wheel does not spin as long with the wheel off the ground this could be due to the grease in the new hub. A properly newly greased hub will not spin as freely as an older wheel with dried out or insufficient grease.