Are centrifugal compressors/turbines less efficient internally, and if so, why?
Internally the big difference is that with axial compressors, it's easy to have a multi-stage compressor to give considerably higher overall compression.
While it is possible to link centrifugal compressors together into a multi-stage engine, it's considerably less common, so most centrifugal compressor engines are limited to the compression they can get from one stage (usually around 4:1).
Axial flow engines get lower compression per stage (usually around 1.2:1), but it's easy to have multiple stages, so engines with 10-15 (or so) stages are fairly common. Given the difference in compression per stage, an axial flow engine typically needs about 8 stages to produce higher overall compression than a single-stage centrifugal compressor.
It is also possible to combine the two. At least to my knowledge, the most common layout in this case is multiple axial-flow stages, followed by a single final stage using a centrifugal compressor.
Here's one paper about using a final centrifugal compression stage, in case you care: https://doi.org/10.2514/6.2019-0944