There is no period/duration-formatter in jsr-310, different from JodaTime. Not every feature of JodaTime was ported to JSR-310 (for example also not PeriodType). And in reverse JSR-310 has some features which are not available in JodaTime (for example localized weekday numbers or the strategy pattern approach with adjusters).
It might happen that Java 9 will introduce some kind of built-in period formatting (read something about this from S. Colebourne).
Conclusion: JSR-310 and JodaTime are not fully compatible to each other, so a lot of work can be required. I would not be so keen on migration as soon as possible. Do you need special features of JSR-310 which are not offered by JodaTime?
Additional note: You should also be aware of the fact that joda period (which includes all units from years to seconds) is not fully compatible with jsr310-period (only years, months, days) or jsr310-duration (only hours, minutes, seconds and fraction seconds).