You have less optional modules because you are doing a joint honours but ring Birmingham and ask if there is a chance of them doing Immigration Law, the optional module list changes every year. A neighbour of mine who teaches at Birmingham taught Terrorism and the Law last yr, but this year taught international Human Rights, so it can all change.
Besides if you wanna go into Immi Law, find vac schemes and mini pupillage's with Immi Solicitors and Barristers, that hands on experience will go down very well in the future if you want to work in Immi Law.
If you do go to Warwick, it still falls with West Midlands so you can use a standard TWM bus pass so there's no extra cost there. if you get the fast train from new street (usually the London train) you can be in Coventry in 20mins and then you can get a bus from the station to the Uni, if you do try to pursue the Warwick route.
NOTE: Warwick's Law and Business is not a qualifying Law degree unless you take a 4th year to do the required modules. Birmingham's Law and business is a qualifying law degree in three years, you want to factor that into the equation.