I'm with the no triggers camp for this particular design scenario. Having said that, with the limited knowledge I have about what your app does and why it does it, here's my overall analysis:
Using a trigger on a table has an advantage of being able to act on all actions on the table. That's it, your main benefit in this case. But that would mean you have users with direct access to the table or multiple access points to the table. I tend to avoid that. Triggers have their place (I use them a lot), but it's one of the last database design tools I use because they tend to not know a lot about their context (generally, a strength) and when used in a place where they do need to know about different contexts and overall use cases, their benefits are weakened.
If both app versions need to trigger the same action, they should both call the same stored proc. The stored proc can ensure that all the appropriate work is done, and when your app no longer needs to support V1, then that part of the stored proc can be removed.
Calling two stored procs in your client code is a bad idea, because this is an abstraction layer of data services which the database can provide easily and consistently, without your application being worried about it.
I prefer to control the interface to the underlying tables more - with either views or UDFs or SPs. Users never get direct access to a table. Another point here is that you could present a single "users" VIEW or UDF coalescing the appropriate underlying tables without the user even knowing about - perhaps getting to the point where there is not even any "synchronization" necessary, since new attributes are in an EAV system if you need that kind of pathological flexibility or in some other different structure which can still be joined - say OUTER APPLY UDF etc.