DRulz, welcome to the forum!
Nobody really knows how long current DVD media will last, regardless of what the marketing departments of optical media companies want you to think.
That being said, DVD media of good quality should last some years unless you are storing the discs in a high temperature or high humidy environment. Some regions of the world have a climate that is not very good for optical media.
A harddrive however can break in a number of ways, and is definitely not something you can expect to last for many years. If your harddrive dies, your entire backup may ge gone in one fell swoop.
Tape can be a good solution for backups, but it is expensive to get a good tape backup solution for that amount of storage, and you are going to need to have the same or a compatible tapedrive if/when you need to restore.
If your mp3 collection is such that you don't modify your mp3 files, but you just get new ones, it might be a solution to make backups on DVD media even though it will take more than a hundred discs for just a single backup.
If your mp3 files are frequently changed, I don't think it will be practical to keep re-burning DVD backups.
You should consider using an external harddrive or two for making frequent backups, and if you have an mp3 collection that is growing (but not changing) you can have another backup on DVD media.