Their latest dispute is over the first patent to be granted on herbicide-resistant crops. Greenpeace has failed to persuade the European Patent Office to withdraw this patent - granted on plants engineered to resist the Basta herbicide.
The group's main concern is that the herbicide is manufactured by Hoechst, which was granted exclusive rights to exploit the resistant crops. Environmentalists argue that this type of 'monopoly' control over genetic resources should not be trusted to any individual, and certainly not to a multinational corporation.
But Plant Genetic Systems, the Belgian company that filed the original patent and settled the patent deal with Hoechst, argues that since the German company is not a seed company it is not in a position to set up a full monopoly - selling both herbicide-resistant seed and the herbicide. Hoechst would need to strike a development deal with a seed company to create the situation environmentalists fear, the Belgians argue.
Greenpeace is particularly opposed to the herbicide-resistance patent since it believes it promotes the use of harmful chemicals. Herbicides should be avoided, the group says, because they threaten human health, pollute the environment and risk the planet's natural biodiversity by killing plant species.
Dr Anne-Marie Bouckaert, director of the technology planning and protection division at Plant Genetic Systems (one of the two companies that filed the patent) disagrees. She said: 'Of course that particular herbicide will be used more often, but it will be replacing other herbicides which are more detrimental to the environment.' Greenpeace is also unhappy because conferring Basta resistance on crops involves adding only a single gene, taken from bacteria. The anxiety is that this increases the likelihood of the gene 'escaping' and passing into species via pollen. This would risk the spread of herbicide resistance to weeds, rendering these less easy to control.
Even Dr Bouckaert concedes this point. 'Because the trait is due to one gene it could more easily be transferred to another species,' she said. But she said that PGS was one of the most experienced European companies testing genetically-engineered crops outside the laboratory.
'There may be cross-pollination between wild species and cultured crops, but in practice you see that it occurs in very few cases.'
She added that the fact that the Basta transformation involves only one gene also makes it easier to track the gene if it does jump into other species.
'Escape of genes in either direction is a problem of which farmers are very aware. Farmers and breeders who pay a substantial amount for seeds need to avoid at any price cross-pollination with wild species. They are therefore already using natural barriers - taking care about which crops they plant next to each other.'
But Greenpeace argues that this is too big a chance to take. Sue Mayer, director of science, said: 'Farmers cannot control who grows what over the hedge.'