At present, I think direct air capture of CO2 followed by reduction to methane and longer hydrocarbons using water-sourced H2 (all without going through the biological photosynthesis) is going to be the long-term winning technology. One main reason is control of the chemistry is a lot easier when you start with uniform small molecules (CO2 and H2) rather than trying to distill off and separate the products of pyrolysis of biomaterials (or even of crude fossil oil distillation and cracking, a similar process).
This isn't to say that if you have a completely renewable energy based power system, that converting agricultural byproducts to useful materials like biomethane, biooil and fertilizer (phosphorous recovery in particular) isn't going to be a plausible approach in specific situations, and the resulting products could have niche markets.
Now, if your goal is to remove CO2 permanently from the atmosphere, that's more difficult. Making materials like limestone (CaCO3) or perhaps carbon fiber is a better idea for that. Bricks of diamond would be even better, but that's a bit more sci-fi still - but possible. Air-captured diamonds would be a cool product.