Hi Pamela, and welcome to the BrickWood forum!
The example in the photo does not look like it has insulation. While it does look like it was based on the Mattone Barile kit, it departs from BrickWood’s instructions at a few places. (It is a beautifully-finished oven, and I’d guess that’s why it caught your eye.)
The good news is that you do not have choose between the cement “look” and having a well-insulated, well-performing pizza oven. The secret is a veneer layer that is applied over the outside of the oven once the inner works are finished. The strength is in the concrete and rebar and stucco. The performance is in the firebrick and hearth insulation and mineral fiber insulation.
The beauty is in the veneer.
I’ve selected several gallery pages at random to show you what is possible when you apply veneer. (Really, only partially random—because they all feature thin layers of brick veneer over the stucco and concrete.)
You’ll see each one of them varies in the way it is detailed (and one has an enameled metal roof!), but they all have one thing in common under their veneer skins: they are all well-insulated and stucco’ed to protect that insulation.
Finishing the stucco shell seems to be a regional choice, but I’d also note that sometimes owners submit their photos when the job is first done. For example, I finished in mid-fall here in New England, and I want my oven operating for next week when it needs to keep a date with a Thanksgiving turkey. So I decided to paint and weatherproof the stucco (which looks really nice as-is), but we’ll move into a “phase 2” next spring as part of the patio that we now obviously have to build around our oven.
This is one of those times when you really can have it all. When you build any of these designs, you get a really solid plan and the pieces you need to make the core oven solid. You get to add the elements to make your oven unique and awesome.
Hope this helps. There is a great community of folks here who have encouraging tips and advice.