I am making a project using 10mm aluminum extrusions. I am trying to connect all three extrusions like the picture below shows and I am going to make my own bracket (in red) out of aluminum since the variety of choices is very scarce for this 10mm size, but I will include a picture of something similar so you can get an idea of what I'm making. I am wondering which arrangement is stronger and more rigid- the left one, or right one? Or is there an even better way to do it?
If you consider the intersecting areas for the left side extrusions as being more evenly distributed, you should be able to expect that the load distribution will also be more even in that configuration. What's equally important is that you require equal strength over the three pieces. In the right side image, if the strength required on the angled portion is less, you can expect similar distribution of forces.
The gusset method you are considering is a common joining mechanism for extrusions primarily because of its ease and strength. You can increase the strength incrementally by adding straps on the inside of the angles attached with the channel nuts.
I would say the configuration on the right would be the best if you cut the top (vertical) extrusion at a 45 degree angle at the bottom where it meets the "45 degree strut". This way all the struts will be flush mounted together. Then you can add side straps and joining plates have the same geometry as the strut-intersection area.