There are a number of things you could do.  You could do plain old likelihood ratio tests or compare AIC's (a penalized likelihood ratio test).  You can use these to compare models.  The AIC's have the advantage of penalizing the 2 level variable for complexity over the continuous variable.

    m1 <- lm(y ~ x_as_2_categories)
    m2 <- lm(y ~ x) # a numeric continuous x
    
    anova(m1, m2)
    
You might want to look at some [basic][1] [papers][2] on this sort of testing.


  [1]: http://ruccs.rutgers.edu/~jacob/teaching/Stats/Papers/glover_dixon_LRs.pdf
  [2]: http://link.springer.com/article/10.1007/s00265-010-1037-6