It looks like it's mostly the lighting. In the example it looks like they're using an environment like an HDR map or something, but in your scene you just have 2 lights. I just added this:
and I got this:
...which is much closer to the example. Of course the other main difference is the tutorial is using Blender 2.8 and yours looks like 2.7x, which will have differences.
He's in Eevee, maybe that setup works fine in Eevee, but in Cycles I think you need at least to mix your Principled BSDF (with 1.00 Transmission) with a Transparent BSDF node. There is a lot of solutions (like use Fresnel in the Mix factor, use Glossy, etc) but it will always be a mix with Transparent BSDF in my opinion.