Personally, I much rather prefer the brim being attached to the actual model, since that's what I care about most. On some of my prints with other programs, if the brim was placed on the outside of the supports, the model actually ended up lifting from the bed since it didn't have anything directly attached to it. So I actually prefer how the S3D brim works right now.
That being said, I've also seen the issue where the support structures have trouble sticking on the first layer. I found what I think is a much better solution for helping the supports stick to the bed, while still maintaining a good brim on the part. You can setup the software right now to print a completely solid first layer of the support structures. That gives you a much larger surface for the first layer of the supports, which helps them stick to the bed. I think that's the best of both worlds, since I still want the brim holding down my actual part, but this helps get the supports sticking better too.
Again, you can do this already with the current software. Just use 2 processes, where the first process is used only for the first layer of the print (i.e. stop printing at 0.2mm or whatever your layer height is). Then change the support infill to 100% for that first layer process.
I've done lots of prints using this exact method and it works really well!