Choosing between chi-squared / logistic regression vs difference of mean tests for studying bankruptices You'd expect more companies to go bankrupt if they have low cash balances.  Of course, bankruptcies can also happen even when you have lot of cash on hand (to terminate labor contracts, etc.).  
The distributions are shown below:  

A chi-squared test shows an association of bankruptcies with cash-on-hand.  I then check the results using logistic regression which actually gives me negative coefficients for low cash balances! (Using LR is fine as I have ~2000 positives for ~150k observations).  
I'm thinking about a simple difference of means test to show that cash balances for bankruptcies differ than those for healthy companies.  Do you suggest any other statistical test that I can use instead?  
 A: I think logistic regression is probably the right tool for you to use.  However, if you only want to establish that the relationship exists, and you ran a chi-squared test first, which was significant, it isn't clear that you need to keep trying additional analyses.  
It is hard to tell from your plots, but the raw numbers of bankruptcies seems to follow the patter of the raw numbers of companies reasonably well.  Thus, the probability of bankruptcy (which is what LR is after) may be fairly similar at each level.  It would be easier to tell if you plotted the proportion of companies that undergo bankruptcy at each level of cash on hand, rather than two plots of raw numbers.  
There are two other factors that you should consider here:  First, a chi-squared test assumes that the levels of your variables are unordered categories, but cash on hand clearly has an intrinsic order.  Agresti has argued that when using an ordinal variable as a predictor, you will do best to make educated guesses about the levels of each category and then use the corresponding numerical values as a single quantitative predictor variable instead of $k-1$ categorical predictors (i.e., dummies).  If your guess isn't perfect (and it really can't be) there will be some measurement error associated with this, but on the other hand, you will gain efficiency by utilizing more of the information available.  In the end, unless your guesses are wildly wrong, the latter effect is likely to outweigh the former.  In you case, I would use the middle of each level of cash on hand for a quantitative coh variable.  Picking a value for the last category >12 is tricky, but a reasonable value is unlikely to cause large problems.  
Second, there may be a curvilinear relationship between cash on hand and the probability of bankruptcy.  So you may want to try adding a squared term.  

Edit in response to comment:
Your chi-squared test assumes that cash on hand is a categorical variable with 12 unordered levels (0-1, 1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9, 9-10, 10-11, 11-12, >12).  But certainly this is an ordinal relationship between these categories.  So instead, use a single quantitative predictor variable with the values 0.5, 1.5, ..., 11.5, 12.5.  This will not be completely accurate, and measurement error in an $X$ variable will cost you power, but it is likely to be reasonably accurate, and will save you 10 degrees of freedom, which will increase power.  You are very likely to end up with a more powerful analysis, and will certainly have a more interpretable model.  
