Is a permanent retainer better than a removable one? What's the difference?

Not necessarily. Permanent retainers, glued to the back of your teeth require special care. The "orthodontic food list" still applies as your glued retainer can become loose from chewing biting into hard-sticky foods. Removable retainers don't have diet restrictions, don't get in the way of brushing and flossing and don't contribute to periodontal disease as glued in retainers can.
First, . First, retention is the concluding stage of orthodontic treatment that holds the final tooth positions in their corrected location. Almost all patients will benefit from some form of retention for an indefinite length of time after treatment. Quite a few patients will need to wear retainers "forever" if they want to keep their teeth ideally aligned. Removable retainers fit over the teeth, some are made of a clear thermo formed plastic, others have wires and clips to hold the teeth in place. Your orthodontist will pick the correct retainer for your problem and determine the amount of time you will need to wear the retainer, generally from full time to nights only to several times a week. Failure to wear the retainers can result in movement of the teeth and a reduction in the alignment. Over time (several years) patients often forget to wear their retainers on the schedule recommended by their orthodontist. This is called "human nature" and results in a relapse (movement of the teeth). Permanent or fixed retainers are cemented to the teeth, either the upper, lower or both. Mostly they are put on the front 4 or six teeth to hold their alignment following treatment. The adhesive is usually the same one that held the braces on the teeth and will last for several years (and sometimes longer). Fixed retainers can break due to the stresses of chewing and sometimes require extra effort to keep clean. They should be checked about every year. Because they are "glued" in place, patients don't have to remember to wear them, so compliance is less of an issue. Not all orthodontists use fixed retainers, feeling that the retention of the teeth is the patient's responsibility. If the fixed retainers are broken or removed, this can also result in relapse. Patients should discuss the various types of retainers available to them, the amount of time that they will need to be worn, both daily and over the length of retention and seek the advice of their orthodontist before retainers are placed. This way they will have the most appropriate retention for their life style and orthodontic problem.