I feel as if I have sufficient knowledge of composite rebar to discuss this topic.
I have certainly formed my own bias of designing with composite vs steel reinforcing over the years based on my experience with them coupled with listening to many many sales pitches from reps, many technical seminars, and attending conventions such as world of concrete.
Our office has been pretty progressive in the use of composite rebar. There is hardly a job that leaves our office that isn't designed using composite bar in some way or another. I have designed several marine structures that appear either on ASLAN's website or on the cover of AASHTO's GFRP Design Guide. Several other projects that are entirely reinforced using GFRP and Stainless Steel. GFRP reinforcing was the first and most prominent material that we used... CFRP to a lesser extent..... and no AFRP due to its lack of availability and little to no apparent benefits over the former 2 counterparts.
Basalt Fiber Reinforcing Polymer (BFRP) enters the mix and appears to show promise. After combing through the technical specifications of the product, you will probably find that it stands pretty much toe to toe with GFRP on all fronts. I believe cost of the 2 is pretty comparable as well. The basalt fibers I believe are manufactured in Russia, if that matters at all. My issue with the product is more on the way that they market the bar. This probably applies to manufacturers of all composite materials but Gatorbar seems to be one of the most egregious offenders. It doesn't help that they had a really obnoxious local sales rep out here who I was never a big fan of. They tout a corrosion proof bar with a strength greater than steel yet they are really only marketing this thing for non-structural slab-on-grade construction as it currently is only available in a #3 size. Unfortunately, they are selling only part of the story, as you can't talk about design tensile strength without also talking about the elastic modulus. After adjusting for reduction factors, you may only have a 20% to 40% gain in strength over steel but with an elastic modulus that is 20%-25% that of steel. In essence, this leads to great concerns with temperature and shrinkage issues and you end up having to design with more FRP reinforcing than steel to account for this difference.
FRP reinforcing, due to its lower density also tends to float in concrete if not anchored down properly. Also, Have you ever seen a 250 lb mason stepping on #3 FRP reinforcing spaced 12" o.c. That bar touches the ground and doesn't always bounce back up.
However, with this being said, there is also a huge benefit as many times this simplifies your jointing detail since you don't have to worry about corrosion at the joints.
For structural applications, you have to really really be careful how you use it. Crushing of the concrete actually becomes your ductile failure mode as rebar rupture is actually considered more brittle. Therefore, there are large strength reduction factors to be taken. Service level crack control most of the time governs. And you really need to be cognizant of deflection due to creep. If you need any ductility at all or have heavy sustained loads, FRP reinforcing should not be a substitute for steel. At this point, seeing that Gatorbar is only available in #3 sizes, it is not being marketed for structural applications, but it won't be long before they establish the material enough to where they can move with it in that direction.
With all that being said, I think FRP reinforcing is great and love to design with it, so long as you understand its limitations. I still prefer GFRP over BFRP as I just don't see anything alluring enough about BFRP to cause me to switch. GFRP has a much longer case-history to learn from and there are several publications dedicated to its use.
ACI 440.1R and AASHTO LRFD Bridge Design Guide....... for GFRP......