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Fastest way to query an XML document

The way to write fast queries against XML documents is the same whether you're using XPath or LINQ: formulate the query so that as few nodes as possible get visited during its execution. It doesn't matter which technology you use: a query that examines every node in the document is going to run a lot slower than one that examines only a small subset of them. Your ability to do that is more dependent on the structure of the XML than anything else: a document with a navigable hierarchy of elements is generally going to be a lot faster to query than one whose elements are all children of the document element.

The absolute fastest way to query an XML document is the hardest: write a method that uses an XmlReader to process the input stream, and have it process nodes as it reads them. This is the way to combine parsing and querying into a single operation. (Simply using XPath doesn't do this; both XmlDocument and XPathDocument parse the document in their Load methods.) This is usually only a good idea if you're processing extremely large streams of XML data.

All three methods you've describe perform similarly. XSLT has a lot of room to be the slowest of the lot, because it lets you combine the inefficiencies of XPath with the inefficiencies of template matching. XPath and LINQ queries both do essentially the same thing, which is linear searching through enumerable lists of XML nodes. I would expect LINQ to be marginally faster in practice because XPath is interpreted at runtime while LINQ is interpreted at compile-time.

But in general, how you write your query is going to have a much greater impact on execution speed than what technology you use.