No such thing as session synchronization for different vendors. You also need to configure everything for both of these vendors, which may or may not have equal feature sets.
But that's incidental to what was my real point, which is that if you do want a separate network, it has to be separate. Tie your two "separate" networks together with integration and you're returning single-points-of-failure back into the mix. Granted, practicality may dictate a couple of those... integrated authentication comes to mind... but you don't want the two separate networks to be all slickly and smoothly integrated for the most part.
Regardless, statefulness is bad of course, and less of it you have, the better you are off - we've seen this time and again: share nothing arch[1], Amdahl's law[2], locks-vs-RCU[3], memorizing tcp flows-vs-IP header hash[4,5], etc... Being able to make decision on current packet/memory access here and now, independently, without having to keep track of other flows/connections/sessions/threads beats alternative approaches every time [6].
[1] https://en.wikipedia.org/wiki/Shared_nothing_architecture
[2] https://en.wikipedia.org/wiki/Amdahl's_law
[3] http://www.rdrop.com/users/paulmck/RCU/hart_ipdps06.pdf
[4] https://tools.ietf.org/html/rfc2992
[5] http://www.juniper.net/techpubs/en_US/junos13.2/topics/conce...
[6] Intel's heroic effort to maintain cache coherency at all cost is a notable exception, although opinions vary wildly on whether this is actually the best thing to do, and how long they will be able to sustain it.