OP, this also depends on what you plan on doing after you land.
Do you have an onward connection? A tight connection?
Do you have a local (i.e. Bath Road) or downtown hotel booked for the day that you land?
Do you have a business meeting the morning you land? The afternoon you land? Business dinner?
Are you seeing a show the night you land?
Are you traveling by yourself? With SO? With family?
I vary my flights and strategies to LHR (and TATL, for that matter) depending on what my plans are after arriving.