Non prescription Reading glasses are made with the same power in both lenses. They are suitable for people whose eyes have the same power in both eyes. Most old people without the problem of myopia or hyperopia prefer to buy them.Also they are much cheaper than the prescription ones. However, most people have different unique prescription, so actually they don't meet your specific need. Prescription Reading glasses are made specially according to your prescription. So it is better to get prescription reading glasses.
Non prescription reading glasses usually have the same prescription for each lens. They are cheaper than prescription reading glasses and its lens can't be replaced if it is broken or the prescription is changed. While prescription reading glasses are specially designed for each individual who have a different prescription for each eye. Since prescription reading glasses are customised, they can also correct astigmatism if required. Though non prescription reading glasses won't harm your eyes, you'd better go to an optician to have an eye exam and get prescription reading glasses.