The biggest growth area is in bioinformatics and work related to genomics and data-rich applications due to advances in biotechnology, e.g. whole genome sequencing. Other areas in which measurement data is available have also undergone expansion, e.g. clinical imaging. The money is in anything where large quantities of data can be collected.
Theoretical mathematical biology has expanded somewhat in recent years but the usefulness of the research in these fields is still subject to much debate (especially amongst practising biologists and clinicians!). There are many reasons but basically we actually do not know that much about the details of many biological processes we are trying to model -- if you do not know what agents and processes are involved math modelling is obviously going to be a bit of a struggle!
Is Biology truly math's next physics is a bad question to ask. Biology is physics -- unfortunately the physics involved in biology is more like the physics involved in meteorology (but probably even more complex!). The systems are large and involve many interactions between multiple agents and processes on different temporal and spatial scales together with no end of internal and external factors which could be involved (some of which maybe unknown). Just as in meteorology, there are biological models that can do a good job of predicting general trends and global patterns in systems but ask a more detailed and practical question and the crude approximations used by these models begin to breakdown (and lets not even begin to think about what our models do when we subject them to a realistic perturbation!
). Hence, my comment (above) about research funders now preferring budding math biologists to actually get experience of working in biology and with biologists during their doctoral training so then you can get into the habit of understanding biology, experimentation and identify aspects of a biological (sub-)system which is amenable to accurate modelling and can be validated.
Basically, the theoretical side of math biology field will grow but just not at the same rate as the applied side that deals with data. It will take us (and the biologists) a long time to work everything out and along the way we are probably going to need to pick up some engineers, computer scientists, physicists, etc because we won't have all the tools and skills to tackle all the problems alone. For the genomics guys, there is big money in academia and industry right now and for the foreseeable future.
P.S. Also beware of paradigm shifting technological advances! For example, I think the field of population dynamics (mathematical epidemiology in particular) is going to fundamentally change in the next decade or two as whole genome sequencing becomes more affordable and quicker and we are able to monitor the spread of infectious diseases by measuring the evolving genetics of the biological organisms involved.