P-value versus Exp(B) value in Cox regression analysis I performed Cox regression analysis for two Biomarkers.  Both were significant (p<0.05).
Biomarker 1 showed higher significance but lower Exp(B)=hazard ratio value than Biomarker 2 (see below).
Biomarker 1: HR=3.06; 95%CI=1.71-5.48; p<0.001 (sorry, SPSS doesn't show more than 3 decimals)
Biomarker 2: HR=6.05; 95%CI=1.67-21.86; p=0.006
Which of the two Biomarkers is a better (stronger) predictor? In other words: what counts more - the P-value or the Exp(B) value?
 A: The two statistics that you mention (p values and hazard ratios) ask different questions, so it is not surprising that they give different answers.
The p-value asks:

If, in the population from which this sample was randomly drawn, the
  null hypothesis was correct (i.e. B = 1), what is the probability of
  getting a test statistic (B) at least as extreme as the one we got in
  a sample the size of the one we have.

The hazard ratio asks:

How different are the hazards of dying for the two groups?

Opinions of p-values vary (to put it mildly!).  My own view is that the question they answer is rarely the one we want to ask.
A: Unfortunately, in terms of predictive power, you cannot tell from this output alone. 
While the fact that Biomarker 2 has a larger estimated HR may lead you to believe it is better, this is incorrect reasoning. The reason for this is that this simple output alone tells you nothing about the distribution of Biomarker 2. To help think about this, consider if we measured the biomarker on a different scale, such that the new values were 10x the current values. Then the fit would be exactly the same, expect that the estimated log-hazard ratio would be 1/10 it's current estimate, despite having the exact same predictive power. So simply looking at estimated coefficients cannot tell you the predictive power of a given biomarker. 
The most straight forward way to compare them is to look at an ROC curve. 
In addition, is there any reason why you wouldn't use both biomarkers? Given that they were both significant in your model, it would suggest that you should get better predictions by using both biomarkers. But perhaps this is unreasonable due to costs of the two tests?
It's worth noting that @PeterFolm's answer above, I believe there is an unstated, but very important, assumption that the covariates are standardized (i.e. all have standard deviation 1). In that case, comparing regression effect sizes is more meaningful. In addition, it's important to note that just because the covariates are binary doesn't mean that they are standardized!
