The difference between a degree in statistics and a degree in biostatistics is very small. Both course have almost similar course outline but the only difference is that biostatistics contain a bit of medical related courses such as survival analysis and more of clinical trials while general statistics contain general statistical topics like probability,demography,population analysis and calculus.
As the name biostatistics sound, graduates with this program end up working for major hospitals where clinical trials,DNA tests and other statistics are conducted. They also work for NGOs, United Nations and government institutions where statistics is needed.Biostatisticians,which is the title given for individuals with biostatistics background, heavily use statistical tools like Stata,SPSS and R Gui.
General statistics has wide range of applications. This graduate can work for government institutions, research firms, stock market, banks, insurance companies and many other institutions where statistics is needed.
If you are about to pursue a statistics related course, I would strongly recommend you pursue general statistics if at all you wish to diversify your skills. But for those who wish to do a lot of statistical modelling and a lot of clinical trials, biostatistics is the best program for you.