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!