Hello Mike,
I am assuming your target is the same lap time as before.
So the RPM will have to be lowered maybe 7% (6-1/2" versus 6" pitch) and the prop efficiency will improve a bit, just as the motor efficiency will drop a bit.
The power required from the prop to run the same lap time will always be the same.
As I said above, the bigger diameter will improve prop efficiency so the power into the prop will be marginally less.
On the other hand, running at a lower % of full drive results in higher peak currents compared to the average, which makes the resistive losses a bit higher.

The result? For one, power consumption will be practically the same.

As for flying ... in most air, you'll probably like it better, provided the turn doesn't suffer.
We eagerly await you assessment of the difference in flight. Let us know, if you are able, over a variety of wind conditions.
Fortunately, the RPM change is easy and repeatable, so you can do A-B testing in different conditions.

Regards,
  Dean

I think the max efficiency of larger prop will stay the same. The shapes are the same, P/D ratio is the same.
Prop will be unloaded in level flight, thus I expect lower efficiency in level, and it will pull harder up hill. So I expect some mAh more compared to 12x6.

You can expect little better line tension overhead (at the same lap time). Properties in wind will depend on the weighth of the model.

But be carefull, use a thermometer to check the motor temperature. You will need to throttle down, and it will need more power, so the temperature will go little up.

Hi Dennis:

I am putting about 2100-2200 mAh back into the battery on a 5 min 30 second flight duration. I fly the full PA pattern plus maybe six laps and some outsides to unwind the lines. Plane is 64 oz 690" Legacy. I am using  5.2 lap as my airspeed goal on 65' lines (eyelet to eyelet). I tried 2650 4S batteries but it was not quite enough capacity. If I cut down the run time to maybe 5 min 10 secs it may be adequate. This is a big plane that can carry the weight of any battery in that 3000-3900 range. I want to try the 2650s again as some local flyers are having success with the smaller cells. I have also tried 5S cells with good success. Luckily my flying buddy has about 30 batteries in the right range that I can experiment with!

Hey, I LIKE operating in a different universe, especially if I can get Seven of Nine to come along on the ride! Wonder what she is powered by...

My thinking is that there is no substitute for careful experimentation, and since we are feeling our way along in E-power why not try something and evaluate the results, both in flight quality and equipment performance or lack thereof? As noted above I doubt I can improve on the 12 x 6 EP but I want to try. I am also not giving up on the 13 x 4.5 EP but my setup seems to be more suited for lower rpm. I don't think I will overheat the motor but will do a 30-second test flight and put the infrared sensor on it and the ESC to avoid an expensive mistake. One more nice feature of E-power.