Although I am definitely subjective on this matter (I did the LLM Energy and Climate Law in Groningen and are now doing my PhD at the same university now), I can at least inform you on the programme in Groningen!
The difference between the different programmes is their focus. For example, in some programmes, the focus is rather on oil&natural resources, while in others, it is more on the entire energy system, or specifically on environmental and climate law. In the LLM programme at Groningen Uni, there are courses on energy law as well as on environmental law and climate law. I'd say the focus is on gas and electricity (Groningen being on top of one of the largest onshore gas fields in the world). However, with the essays and thesis that you have to write, there's suffiicient room to research the subjects/combinations that you find most interesting. For example, I wrote on the electricity balancing market, but also on the regulation of gas infrastructure, combined with human rights! (and now I'm doing a PhD on the legal aspects of offshore electricity grids!
Concerning the PhD: great idea, there's a lot of research to be done in the field of energy and environmental law! At Groningen Uni, PhDs are part of the Groningen Centre for Energy Law. Subjects we are currently working on include the regulation of offshore wind energy, power to gas, smart grids, technology neutrality etc. Many different things!
If you'd like to, you can glance through the different subjects we are researching here (by clicking on the name of a PhD researcher, you should get more info on his/her research): http://www.rug.nl/research/groningen-centre-for-law-and-governance/onderzoekscentra/gcel/medewerkers-gcel
I hope this information can help you a bit in choosing which LLM suits you best! If you have any more questions about the programme or the application procedure, feel free to contact me! :)