It is, indeed, a different setup.

Recording a single PART, like a Guitar, from the MOXF to an external MIDI recorder requires the following changes and setup:

1- You must synchronize Clocks _ make Cubase AI7 the master clock and set the MOXF to "auto" which will allow it to follow Cubase's tempo. You still will be responsible for coming in on the beat, but the tempo of the controlled arpeggio phrase will lock to the master clock.

2- You must setup Local Control ON and defeat the MIDI Thru feature _ When recording Note data generated by an arpeggio phrase, you are interested in recording only the Notes of the arpeggio phrase, NOT the trigger notes, as you normally would. You may be holding a E7 chord for four measures... What you actually want to print to Cubase is the notes generated by the arp, (Not a whole note chord tied for four measures!)
So the LOCAL CONTROL = ON is necessary so that your trigger note (key presses) go to the Arpeggiator. The Arpeggiator analyzes your trigger notes and generates its phrase data based on the built-in chord intelligence feature. This in turn triggers the MOXF tone engine. You then must turn the ARP OUT SWITCH = ON and set a MIDI channel for the data to travel OUT on. By setting this SWITCH ON, the arpeggio sorted notes travel to Cubase, instead of your trigger notes.
Next in Cubase you must setup a MIDI TRACK to Receive this stream of notes, but during recording of this data, you must defeat the MIDI data from returning to the MOXF!!!
Because incoming MIDI data will trigger the ARP (again)

Okay that all said, this is what needs to be done to record normal, note-type arpeggio phrases. There are some arpeggio phrases that are simply controller data, others that are utilize velocity limits, which present a unique problem for external devices. So there can be no one answer that applies to all arpeggios.

But you mentioned a Guitar Arp, which is a normal, note-type arpeggio.

From SONG/PATTERN mode
Press [MIXING]
Press [EDIT]
Select the PART 1-16 that contains your Guitar Voice
Press the dedicated [ARP EDIT] button to the left of the screen
Here you can use the Function and SubFunction buttons to assign and select the Arpeggio parameters.
[F6] OUT CH is where you find the Arp OUTPUT SWITCH and CHANNEL assignment.

You can setup the MOXF's Clock, Local Control, and track switches by simply holding [QUICK SETUP] + [B/2] button... This selects the "ARP REC" template. This makes all the appropriate settings for clock and transmit for the MOXF Tracks.

In Cubase go to TRANSPORT > PROJECT SYNCHRONIZATION SETUP... > MIDI CLOCK OUT > DESTINATION = Yamaha MOXF6/MOXF8-1 (port1)

Make sure you use the Cubase Click's count-in... It will still be your responsibility to come in on the beat ... The entire arp phase will be off by the distance you are early or late (if you get my meaning) it will be diligently early or late based on your trigger event, and remain so. It is easy enough in Cubase to clock shift events earlier or later.

Make sure the MIDI TRACK's OUT port is temporarily set to "Not Connected". Midi IN from the MOXF, but Midi OUT should be set to "Not Connected" during the real time record process. Once you have recorded the Arp, please set the MIDI Out to playback the guitar Part you desire.
And don't forget to select the QUICK SETUP appropriate for what you want to do next.

In other words, return your setup to normal for what you are doing. Recording Arps is different!

Thanks for you quick response! Looking forward to trying it out!