You know, a stick blender (aka immersion blender) will do all of these things except chop (and its 90 per cent easier to wash up and takes up little space!). Plus, you can use it straight in the pan in which things, such as a soup, are cooked. Stick blenders are quite cheap. I gave up using a food processor a while ago and now use a stick blender and occasionally a mini-chopper if I want to mince things finely. But if you use a food processor a lot for cake-making or for chopping large quantities then I guess a a processor is better. I'm probably teaching my grandma to suck eggs here, as the saying goes!
Stick blenders are usually sold with a tall beaker which contains any splashes if you are pureeing something very liquid, like fruit. If you don't have a stick blender I'd highly recommend it even though you may use a processor for chopping large quantities. You'll find that you can use it for many of the tasks that you mentioned, including pureeing beans - which can be done in the saucepan! And it saves so much washing up!
the hand blender (as I know them) is great, but it is not for smoothies. It is more for soups that are part pureed and still have a few lumps in them so the veg (or other stuff) is still recognisable.
Are you meaning a stick blender as I know it, when you refer to a hand blender. There is no problem making the smoothest purees or smoothies with a stick blender. I know because I've done it! Demo here:
in the picture above that you posted, the one on the left is what I know as a hand blender, because you use your hands to move it around the pan. If the pan is too big, it can take quite a bit to actually get everything lovely and smooth and in my experience if you wanted everything smooth, then you either needed to use the tall thin jug that came with it which was really easy to knock over, or it was quicker to use a liquidise (blender in USA). Of course the quality (and therefore expense) of the hand blender might have something to do with it, but mine was a kenwood one which were generally OK.
