Based on this post I wanted to integrate Sowmyan's findings into the U2U CAML Query Builder. But I came to the conclusion that I can also update a user column in a list using the UpdateListItems method of the Lists.asmx web service with following query:

<Batch PreCalc='TRUE' OnError='Continue'>
   <Method ID='1' Cmd='Update'>
      <Field Name='ID'>12</Field>
      <Field Name='AssignedTo'>9</Field>
   </Method>
</Batch>

I don't specify a field type and for the user column I only specify the ID of the user I want to assign the task to.

To retrieve rows using the GetListItems method I couldn't use the ID of the user but I can use his/her name:

   <Where>
      <Eq>
         <FieldRef Name='AssignedTo' />
         <Value Type='User'>Karine Bosch</Value>
      </Eq>
   </Where>

Luckily it doesn't always need to be complicated