Ahh the good old debate, just what does green mean? Is it worse to have petroleum products in X or have used petroleum to transport products a longer distance without them in it..
As I am sure you know, true linoleum is made from natural materials like linseed oil, wood flour, mineral pigments, and is mounted on jute backing and is naturally anti-bacterial and biodegradable.
Personally I would lean towards a true linoleum over vinyl if possible and it meets the needs of the clients.
For more information:
Read "Should we avoid the vinyl linoleum? We need to replace a little bit of linoleum in our back door entry way and under our kitchen sink." a Q&A answered by David Bergman.