Pros:
Better data utilization of link, i.e. 1460/1518 = (about) 96% vs. 8960/9018 = (about) 99%, an increase of about 3% if you use jumbo.
On many devices, improved throughput as PPS demands decrease as packet size increases; recall this may be true for your 2960X, but also recall, 6807 may have consistent PPS rate regardless of packet size; likely the 2960X is wire-rate, for all ports, even with minimum size packets, so this wouldn't matter, might (probably unlikely, though) make a difference on the 6807 if sup and its DFCs, if any, PPS is being exceeded because of lots and lots of minimum size packet traffic.
Cons:
There's no standard for what max MTU should be for jumbo. Most vendors support 9K something, but the "something" can differ between platforms and cause MTU issues.
Jumbo packets increase store-and-forward, per switch, latency. (Also why, I suspect, cut-through switching has reappeared.)
Jumbo packets, if corrupted, have bigger impact (whole, larger, packet needs to be resent). In theory, corrupted larger packets are more likely to slip past packet/frame validation w/o detection (not a huge risk increase, at least for an Ethernet frame's FCS).
New chances to create in-flight fragmentation.
New chances to mismatch MTU on same L2 segment.
More "care and feeding" required.
Summary, unless you really, really need the extra 3% increased data transfer capacity, for most use cases, jumbo not worthwhile.
One use case where jumbo is "nice", if you have tunnels that would normally fragment 1500 byte packets (due to encapsulation overhead), jumbo allows such encapsulated packets to be sent without fragmentation.
