I've used a variety of non-strip/hard waxes from both companies, but not the Lycon strip waxes. It's a little difficult to say "which is best" as a lot comes down to personal preference and experience with the products.
It's no secret that my personal preference is Perron Rigot and I use their full range in the salon and on my training courses - I'm happy to share why I like the line, but I do train with the stuff so I'm a bit biased!
I will certainly say that BOTH lines give fantastic results if you take time to learn about the waxes and how to use them correctly. Lycon and Perron Rigot non-strip waxes are really quite different to the old-style hot waxes, and to get the best out of them it is worth investing some time in learning how to use the products properly.
Both companies will send you samples if you ring and ask. I'm not 100% sure who the new UK Lycon distributor is - it used to be Beauty Products UK until very recently, but I think that Strip in Notting Hill have now taken over. Thalgo distribute Perron Rigot and you can reach them on 020 7512 0872.