Ugh
Wery difficult questions and therefore it doesn't have a single correct answer. I don't anymore use the Jython Robot Framework but I did use it in the previous work. Also I don't have any statistics how popular the Jython is compared to the Python.
The core framework is same for Python and Jython, but the difference comes from the libraries. Based on the gut feeling, there seems to be lot more open source libraries available for the Python than for the Jython. But I don't have any real statistics to back up my claim.
Customisation is quite a vide term and I don't know what you mean by it. Do you want some custom reporting or do you want to extend the library in some way? Or something totally different?
Generally speaking Robot Framework customisation quite easily. It can be customised by developing libraries to interact with your application. More details from libraries can be found from the user guide [1]. Also the remote library interface allows user to create libraries with any programming language that supports XML-RPC.
When I did live in Jython world I did love the maven integration, which is a big plus if you happen to use it. It did make the usage of the Java libraries really easy.
But I depends what you need but we might be able to help you better if you could explain better your needs.