With Juicebox-Pro, you would be able to create the gallery from your image but not the rest of the page. Juicebox-Pro is an image viewer/web gallery and not a complete web design package. You would need to somehow create the web page (either manually or using web design software) and then embed your Juicebox gallery in it following the instructions here.
Showkase, on the other hand, is able to create a complete portfolio website.
Showkase has full support for Juicebox-Pro (and SimpleViewer-Pro) and the galleries can be created within the application itself in a web browser interface (or created with JuiceboxBuilder-Pro and imported).
Showkase can also create non-gallery pages (About, Basic and Contact pages) where you can add information about yourself (or any other content you like).
It may not be possible to exactly replicate the web page from your image using Showkase but you would certainly be able to include most of the features (using a logo in your site's header, having a menu for users to navigate throughout your site, contact details, etc).
All of this is done automatically within the Showkase interface without the need for any manual coding at all.
Please take a look at our demo Showkase sites to see what can be achieved with Showkase.
Showkase can be purchased as Showkase-Standard (which comes with Juicebox-Lite and SimpleViewer-Standard, the free versions) or Showkase-Pro (which comes with Juicebox-Pro and SimpleViewer-Pro).
(The only difference between Showkase-Standard and Showkase-Pro is the bundled viewers.)
I hope this information helps.