Buy whichever you like. Mostly it will be subtle differences in feel between the two, but you can set most suspension up to feel the way you like anyway.
Like any product, the placebo test will be people claiming huge increases in performance, when between most high end products, it just isn’t the case any more.
The Idylle is slightly lighter if that’s important.
For me, as a former BOS shock owner I would be looking at the Fox. As part of the ownership prospect I think you need to consider other factors such as servicing & spares availability.
This is where BOS falls down massively. No product for months at a time, including spares and erratic communication from R53 at best. TF Tuned tried to make BOS work for years, but had to let it go in the end due to the failings from BOS in France.
And let’s face it, in 99.5% of instances, the limiting factor in the equation is the person on the end of the suspension, not the suspension itself.