Does PBR incur a performance penalty by design? I am wondering if the various PBR models used in modern game engines for real time are heavier in terms of computation, that more classic approaches to rendering.

Worded differently, is PBR just a different way to organize one's rendering pipeline, or does it add serious complexity (especially in regards to lighting) ?

Depending on the answer, what would be the bottleneck for a low-resource implementation ?
As mentioned in this answer, Physically-Based Rendering isn't a set number of things. It's a concept. It's akin to saying something is 'Environmentally Friendly'. There are many different techniques to be environmentally friendly and someone can implement those techniques to varying degrees. The same is for PBR.

In the end, Physically Based Rendering is just that, based on Physics in some way, shape, or form. One of the most basic 'physical' rendering techniques I can think of is using Lambert shading. While you may say, "Well that doesn't take into account specular light, or etc, etc. etc.", I agree. Lambert shading is a crude representation of the physics of light. But, pedantically, it is PBR, because it is based off the physical observation that light intensity decreases with viewing angle.

A renderer can implement as many, or as few PBR techniques as they choose. Some can be very computationally expensive, others, quite cheap. They can also choose to enable or disable certain techniques for different targets. For example, UE4 has a different set of techniques for mobile games, than for high end PC games. 

Now, that all said, when today's modern renderers talk about being "Physically-based", they are generally referring to using a modern BRDF, generally some form of Cook-Torrance, and physically plausible inputs. Inputs being: materials with physically-plausible color values and lights with physically based intensity values. 

Using a modern BRDF can be very computationally expensive, but, there are many approximations that can make it more friendly.

Using physically-plausible inputs is generally not that difficult to implement on the renderer side, rather it's more difficult for artists. IE. teaching them what the different material values mean, and what are physically plausible values. This can be a huge task, depending on your artists, as seen in the presentations here, here, and here, for example. In my opinion, this is the hardest task in switching a studio.

Edit:

One last issue, as brought up by @NathanReed in the comments:

Implementing a modern BRDF in the shader doesn't necessarily immediately make the rendering better. In many cases, it can make other parts of the pipeline a glaring issue. Below are some additional things that are important in getting the most out of a modern BRDF:


HDR lights and doing all rendering calculations in HDR
Gamma correct rendering
Indirect lighting of some kind (skybox lighting, static environment probes, screen space reflections, etc)


This is huge for metals. Metals have no diffuse reflectance, so most of the surface of the metal will be black if you don't have indirect reflections
This is also one of the more difficult things to get real-time, especially for dynamic scenes.