Complete academic discussion side trip: I’m often bemused at the buzzwords we adopt from time to time. “Modern” is one of those recent en vogue terms. And can have condescending undertones. What characteristics are applicable for “modern”? If something gets labelled as “more modern” what judgements might we make? What capabilities or features can we assume? Will such assumptions be accurate?
May I humbly suggest to avoid labels that are not well-defined and instead explicitly note the characteristics that are useful for decisions. 
Regarding the OP’s question about “what the best option is” consider that “best” is always subjective. What works for one in a given situation may not be good for another, even if the situation is similar.
We’ve used the pub.storage services without issue, though our scenario may be a bit simpler than yours – storing the timestamp of the “last record seen” to be used in the next scheduled run as the “get records modified after time”. No possibility in our case of multiple threads working on the same keyed object.The locking aspect was not a significant concern. We always unlock right after a get, and use the implicit locking provided by put.
Selecting cache or storage facility might simply be an arbitrary decision. They are both intended for the same purpose. From the docs:
“The pub.cache services are a tool for maintaining state information for the short term” – p. 80 in Services Reference
pub.store – “These services are a tool for maintaining state information in the short-term store” – p. 928
The former is implemented using Terracotta Ehcache while the latter uses the “IS Internal” DB, which can be shared by IS instances with or without an IS cluster (we have it without – IS Internal defined to use the same DB and user in 2 instances).
Which to choose depends in part on what your environment currently has set up. Beyond that, it will depend on which you prefer based upon your assessment of the services. Both can do the job.
#Integration-Server-and-ESB#Flow-and-Java-services#webMethods