Sorry to say I don't fit your category of "direct experience using both", but I do have a 16702B and am reasonably well versed in its capabilities.
The MS-500, if I'm reading LeCroy's documentation correctly, is a timing analyzer. It samples the digital inputs at a fixed interval (like almost all MSO logic analyzers). The 16702B has timing analysis too, but it can also operate as a state analyzer. The state analyzer only captures data on the transition of a clock input, and optionally when configurable conditions are met.
Both would be suitable for looking at the timing relationships of a lot of digital input signals, but the 16702B would make better use of a given amount of analyzer memory since it's one location per interesting state event, and better at sophisticated triggering based on program flow. Many of the 16702B acquisition cards have a 16 sequence trigger state machine that controls capture and trigger and is programmed through the GUI.
The 16702B was really designed for the era of exposed parallel buses, and doing debugging and code flow analysis while developing those systems. It has a lot of API hooks allowing you to roll your own tools if you wanted something like a custom opcode or protocol decode. It also has analog scope cards where you can display up to 8 channels along with the digital analysis. The scope card can come in handy, but unfortunately are very limited due to their capture buffer of only 32k points.
If one of your requirements is serial decoding, the 16702B has rudimentary trigger and decode on some types of serial streams. The triggers are constructed via the GUI, and under the covers actually use the 16-level state machine.
But I think you would be disappointed in the small breadth of protocols supported, and the clunkiness of the interface compared to more modern tools that are targeted for microcontrollers and their plethora of serial interfaces. I have never opted to use the serial capabilities of the 16702B and instead reach for a Saleae logic analyzer, which I'd highly recommend as a companion for any scope. Even one that's already an MSO.
If you haven't already found it, you can read more about the 16702B here:
http://literature.cdn.keysight.com/litweb/pdf/5968-9661E.pdfThere's a section in that document with an overview of the (limited) serial capabilities.
All the option licenses, including serial analysis, are available for free and with the permission of HP/Agilent/Keysight, provided they are used only for non-commercial purposes. There are a lot of opcode decoders (in HPAK parlance "inverse assemblers") for older 8 and 16 bit processors, many posted to other threads in this blog.
That link seems to be broken. Hopefully it will get fixed. Try this copy:
http://www.libertytest.com/assetmanager/uploaded/pdf-2010823-94153-hp_16522a.pdf