I have a potentially really dumb question
Not dumb at all. I am trying for years to get some quantitatively answers to these questions.
Some reactions point to the different algorithms used. This is true, but the fact is that the NT algorithm used by NSIDC almost always calculates a lower sea ice concentration than the BT algorithm used by Jaxa. That explains a lower area (NSIDC area about 300k below Jaxa), but not why the extent is higher.
Now it is important to realize that extent is inherently and by definition depending on the resolution of the sensors and the grid in which sea ice concentration is represented. Extent, by definition calculates the open water in grid cells with 15% ice or more as 100%. High enough resolution to be able to resolve the open water would not and give the same amount of ice as area.
Higher resolution also reduces "false coastal ice" from land spillover. If not effectively filtered this will increase extent of the low resolution product.
* Why is the difference so big say between IJIS/NSIDC right now?
Resolution and land spillover, that will have to be my answer to your first question.
Best advice is to compare likes with likes. So Jaxa with Jaxa and NSIDC with NSIDC.
* Could I possibly have some enlightenment on the pros/cons of these different sources?
Jaxa uses the better sensor (better resolution and accuracy), the algorithm is probably better (but opinions differ), but that is only true for AMSR2 data available since August 2012. Earlier dates are using different satellites, the influence of that is unknown to me.
NSIDC on the other hand has taken care to produce extent data that can be reliably compared over the longest time span available (since end 1978).
* I wouldn't mind your opinions on which ones you prefer (and why)
I depends, reason given above. Jaxa will produce the better day-to-day numbers, but in comparing them with pre-AMSR2 years I hold a healthy skepticism.
For climatology relevant work there is only NSIDC.
NT=Nasa Team algorithm
BT=Bootstrap algorithm