Not so hard, some of it easier
* A printer
System - Printing. Find printer on network, select type, print test page. Done. No loading crapware of a CD etc.
* A scanner
Xsane just finds the scanner on the network. Never used a USB attached one, but assume same.
* A DSL modem or router
Eh? Why should you need the crapware to set this up, which in windows XP/Vista leaves doubt as to which of the several icons on the taskbar actually control networking? How many times does it 'just stop working' on windows? Type 192.168.2.1 into a browser and set it up. A bit more difficult than using a driver/installer CD but once it works less likely to break.
* A digital camera
Connect, open photo software when prompted, import new photos. Done.
* A digital video camera
Plug in via USB, Open folder when prompted, double click vid, plays with VLC or MPlayer. Easy.
* An MP3 player
Sync with Rhythmbox automagically.
* A smartphone
Drag and drop stuff to it, easy. Much easier than using iTunes. Easier to get photos off an iPhone too.
Of course this comes with a couple of assumptions,
1) You installed a distro with all codecs installed.
2) All hardware is supported. A lot is these days out of the box, so is in fact easier to use than on windows. When the hardware is not quite working it does take a bit of tweaking to get it working, but then there are similar intallation problems with windows too.
The main problem is that you have to start messing under the hood sometimes, e.g. mousepad is unusable, disable tapping of it in order to be able to use it. Which means hand editing config files. Or changing boot parameters so that you get something other than a black screen etc. I would like to say that once fixed in linux it stayed fixed, but this is not the case anymore. The EEPC901 wifi driver needs to be recompiled from source with every new kernel for instance, which for a non techie means no chance!
So, to sum up, if you get lucky or buy wisely, then it is EASIER with linux. If not it is probably more difficult.