I have only the original Stripology ruler, so I can't compare it to the June Tailor (other than I've handled the JT version when visting Joann's in the past and agree that it's much thinner/flimsier than the Creative Grids ruler).
That said, I don't use my Stipology ruler much, and I'm very glad I didn't buy it at full price. I've found that my cutting woes weren't due to a lack of the proper tools, but were related instead to my folding. With the Stripology ruler, you have fold a piece that's the full width of fabric at least twice to actually get it narrow enough to fit. If you don't have the fabric folded perfectly straight, your strips will not be straight, regardless of any fancy tools you have (at least, in my experience).
At this point, I use my big 24 1/2 inch long ruler to make strips with, which I've found to be much more accurate because I only have to get one fold just right. I also don't have a really good surface to cut larger pieces of fabric, so this could be a contributing factor to my wonky cutting.