I would recommend setting up memcached or even varnish (seems to be the new craze) as both would simplify load balanced cache and session sharing issues your experiencing running both servers as file system.
To quote the magebase article (NOTE: the same applies to cache):
Memcached session storage takes a bit more setup than either of the previous two options, which is probably why it’s not considered a ‘normal’ option during Magento install. For starters you need a Memcached server running.
Once you have it up and running, the memcached session storage offers
a number of benefits. Firstly it is very cluster friendly. The session
data can be shared by any number of webnodes, and to make things even
better you can easily add more memcached server nodes so that even
your session storage can be scaled to handle many 1000′s of concurrent
sessions*. Secondly, it is (or can be) separate of the database and
web node entirely, which offloads the work of storing sessions from
busy nodes in a high-traffic environment.
More details on choosing a session storage for Magento:
http://magebase.com/magento-tutorials/magento-session-storage-which-to-choose-and-why/
More details on setting up Varnish to work with Magento:
Getting Varnish To Work on Magento