Praise be to Allah.
Organic meat is meat that comes from livestock and poultry that were raised in a specific manner, according to certain conditions and guidelines, similar to nature, whereby they are raised and fed with food that is free from chemical additives, antibiotics and hormones, and that are also not genetically modified. End quote from http://bit.ly/2AYuM5V.
Non-organic meat is no different from organic meat, apart from the possibility that it may contain some harmful elements, as a result of the manner in which it was raised and the type of food with which it was fed.
Whatever is originally deemed to be permissible cannot be forbidden just because it is thought that it may be harmful, unless we establish that a particular thing is likely to do more harm than good.
Shaykh ‘Izz ad-Deen ibn ‘Abd as-Salaam (may Allah have mercy on him) said:
If there are both benefits and harms, then if it is possible to attain the benefits and ward off the harms, then we should do that, following the command of Allah, as He, may He be glorified said (interpretation of the meaning): “So fear Allah as much as you are able” [at-Taghaabun 64:16].
If it is not possible to ward off the harm and attain the benefit, then if the harm outweighs the benefit, we should ward off the harm and not worry about missing out on the benefit. Allah, may He be exalted, says (interpretation of the meaning): “They ask you about wine and gambling. Say, In them is great sin and [yet, some] benefit for people. But their sin is greater than their benefit” [al-Baqarah 2:219]. He prohibited them because their harm is greater than their benefit.
If the benefit is greater than the harm, then we should attain the benefit despite the fact that there may be some harm. If the harm and benefits are equal, then we should refrain (until more is known and the issue is settled).
End quote from Qawaa‘id al-Ahkaam (1/136).
With regard to non-organic meat, its benefit is proven or most likely to be there, whereas there is some doubt as to whether it is harmful, so the known benefit of it is not to be prohibited just because it is assumed that there may be some harm in the future.
The benefit that is established and immediate takes precedence over harm that is assumed will arise in the future.
End quote from Nihaayat al-Muhtaaj by ar-Ramli (6/181).
With regard to it being better, it is not regarded as being better on the basis of shar‘i evidence, and it is not mustahabb to eat this kind of meat to the exclusion of the other kind. Both are things that Allah has made permissible, and there is no blame on the one who eats this kind of meat or does not eat it.
But if a person chooses for himself a specific type of food, because he thinks that it is safer for him and is less likely to lead to harm, then there is no blame on him for that. Rather what is required of the Muslim is to maintain his health, strength and vitality, so long as he does that within Islamically-acceptable limits, and it does not go to the extent of intrusive thoughts (waswaas) or extravagance, or forbidding something that Allah has permitted, because of the mere possibility of it causing some harm, or to the extent of denouncing people who eat it.
And Allah knows best.