In terms of LINQ processing time the difference should be very very small, it depends on the shape of the document. If you are looking for an attribute on element with many attributes it's going to be slower, so if you know you will have just that one attribute you're looking for it will be fast. Same goes for elements. So if the sample above is representative, the faster one would be the attribute as there's just one attribute, but there would be two elements if you moved the name to the element.
Second consideration which is probably more important is parsing speed. You will need to parse the document first to be able to search it. Parsing speed depends mainly on the number of characters it has to process. So the longer the input document (in bytes), the longer it's going to take to parse it. In this sense attributes are a bit shorter than elements (usually). Also the bookkeeping the parser has to do is little bit less for attributes than elements (especially if you have just one attribute on an element).
But as with anything about performance: Measure It. That's the ultimate answer.