Unless you're laying out lots of Views (e.g. in a ListView), the performance of choosing between LinearLayout or RelativeLayout is negligible. Pick whichever is most convenient to use for the job, and worry about performance only when you need to.
And here's what the official docs about Creating Efficient Layouts says about performance of RelativeLayout and LinearLayout:
Sticking to the basic features is
unfortunately not the most efficient
way to create user interfaces. A
common example is the abuse of
LinearLayout, which leads to a
proliferation of views in the view
hierarchy. Every view — or worse,
every layout manager — that you add to
your application comes at a cost:
initialization, layout and drawing
become slower. The layout pass can be
especially expensive when you nest
several LinearLayout that use the
weight parameter, which requires the
child to be measured twice.