Difference between Monitor out and Direct out...?

The differences are in the Kemper manual... It's helpful to read it.

Monitor Out section

(2)
Use this mono output to connect the KPA to a stage monitor with its own level controls. This output also
has its own GROUND LIFT.
You can also connect this output to a power amp and a regular guitar cabinet. In this case, you need to
switch the cabinet simulation off, using the soft button "Monitor Cab Off" in the master page, to prevent
unwanted coloration created by running a speaker-emulated signal through a guitar cabinet.

Direct Output/Send

(3)
This carries the direct output signal in glorious mono. The main purpose for this output is to feed signals
into the reference amp while profiling. But it can do more than just that: you can also use the DIRECT
OUTPUT in combination with the RETURN INPUT to create an effects loop. In this case, the DIRECT OUT-
PUT becomes a mono send.
If you're not using this output as part of an effects loop, it will carry the original guitar signal. So, if you
want to record your guitar dry, connect the DIRECT OUTPUT to the recording device or audio interface
input.

From the Main Manual 8.5:

page 41: If you select the option “Monitor Stereo”, MONITOR OUTPUT and DIRECT OUTPUT become one logical pair of stereo outputs.

page 42: DIRECT OUTPUT/SEND (3) This carries the direct output signal in glorious mono. The main purpose for this output is to feed signals into the reference amp during PROFILINGTM. This is not its only purpose, however: you can also use the DIRECT OUTPUT/SEND in combination with the RETURN input to create an effects loop. In this case, the DIRECT OUTPUT/SEND becomes a mono send. If you're not using this output as part of an effects loop, it will normally carry the original guitar signal. So, if you want to record your guitar dry, either connect the DIRECT OUTPUT to the recording device, or to the input of your audio interface.

Oh BayouTexan was faster!

From the manual... I would use the main out for your PA.

MAIN OUTPUT (4)

These are your main stereo outputs. Use these outputs to connect to a mixing desk in a recording studio, or to the front-of-house mixer in a live situation. These outputs deliver the entire Rig: amp, cabinet, and all effects. You have a choice of XLR (balanced) or quarter-inch TS-jacks (unbalanced). The XLR outputs are protected against 48V phantom power fed by a mixing desk. However, you should avoid feeding phantom power into the PROFILER if you want the best audio quality. Like all inputs and outputs, it offers a ground lift in the menu of the Output Section to prevent a loop hum.

MONITOR OUTPUT (5)

Use these outputs to connect the PROFILER to a powered stage monitor for mono, or two powered stage monitors for stereo. These outputs have their own level control and ground lift in the menu of the Output Section.

You can also connect this output to a power amp and regular guitar cabinets. In this case, you need to switch the cabinet simulation off, using the soft button “Monitor Cab Off” in the Output Section, to prevent the unwanted coloration that would result from running a speaker emulation through a guitar cabinet.

Bypassing the cabinet module can also be done by simply pressing the CABINET button. However, there are two differences compared to enabling “Monitor Cab Off”: • Bypassing cabinet is an individual setting to each Rig, unless you lock the cabinet module in its “off” state. Monitor Cab. Off is a global setting. • It will bypass the cabinet module for all outputs, whereas "Monitor Cab Off” will only affect the signal routed to the MONITOR OUTPUT.

✓ The functions described in the above paragraphs are only the standard settings. You can change the signal sources individually for each output in the Output Section; e.g. you can set the MAIN OUTPUT to only deliver the wet delay and reverb signal, while one of the SEND outputs carries the pure amp sound without effects. There is also a tutorial video specifically about the Output Section and setup for recording available on: http://www.kemper-amps.com/video

DIRECT OUTPUT/SEND (3)

This carries the direct output signal in glorious mono. The main purpose for this output is to feed signals into the reference amp during PROFILINGTM. This is not its only purpose, however: you can also use the DIRECT OUTPUT/SEND in combination with the RETURN input to create an effects loop. In this case, the DIRECT OUTPUT/SEND becomes a mono send. If you're not using this output as part of an effects loop, it will normally carry the original guitar signal. So, if you want to record your guitar dry, either connect the DIRECT OUTPUT to the recording device, or to the input of your audio interface.

✓ The functions described in the above paragraph are only the standard settings. You can change the signal sources individually for each output in the Output Section; e.g. you can set the MAIN OUTPUT to only deliver the wet delay and reverb signal, while the DIRECT OUTPUT carries the pure amp sound without effects. There is also a tutorial video specifically about Output and setup for recording available on: http://www.kemper-amps.com/video