Personally, I would not use either.
The comment about flash drives losing their guts is not correct. Flash memory typically has a retention period of about 100 years (at 25 degrees C). The more you use it the sooner you wear it out. However, typical write/erase cycles for flash is about 100,000 to 1 million so you are unlikely to wear out a flash drive in under a few years (if then). [It may be that some very cheap Chinese rubbish flash drives do lose their guts but if you buy a reputable brand this should NEVER be a concern.]
DVD's are slow, and the data retention period for burnable ones is not all that good - 1 to 5 years before you start to get some noticable degradation. There are a series of papers and studies on the net you can find that mention this.
If you have only small amounts of data to back up, then a flash drive, or better, several used in rotation, is fine.
If you want more than that (ie a few GB) then, like the history of computing, there aint no way to beat a spinning hard drive. These days hard drives are so ridiculously cheap that you can buy 1 TB fort about US$50, stick it in an external USB or SATA enclosure for another $50, and you have a VERY BIG backup device. Do 2 of these and use in rotation, locking them in the cupboard or somewhere safe (or off site) when not in use.
When you consider that a 4 GB flash drive is about $6, and 1 TB hard drive is $50, it makes little sense to even try and use flash drives for more than about 10 to 20 GB of backups. The hard drive should keep you going a long time, and whats more the prices keep coming down so if (when) you need bigger it won't cost an arm and a leg.