They both have been in the league since 2003, so they're about the same age. Both have about the same number of career starts.
Burleson's career 13.5 yards-per attempt is an upgrade over Johnson's career 12.5. Burleson has one season with more than 1000 receiving yards (1006 in 2004), another season over 800 (812 last year). Johnson has been very consistent in the 400's-500's, with one exception--740 yards in 2006.
As far as touchdowns go, Burleson had two 9-TD seasons (2004 and 2007). Otherwise, both receivers are in the 1-4 range for their careers. Hopefully whatever worked for Burleson those two years he can recreate for us, and he can be more of a scoring threat.
I don't have a chart for receptions, but it's just like TD's and Yards--Burleson's best couple of seasons are far better than Johnson's, but their numbers are otherwise pretty similar for the rest of their careers. Burleson's best seasons in receptions were: 68, 50, and 63, but the rest of his seasons were 30 or less. Bryant Johnson is consistenlty in the 35-49 range his whole career. Careerwise, Johnson has 290 receptions to Burleson's 263.
Summary: Burleson brings some more upside, but more risk of very low production from injury, while Johnson is consistently mediocre.
data (source: www.profootballreference.com)