With the availability of compact USB memory sticks with much, MUCH higher storage capacities is there still any use-case for taking periodic, incremental backups on DVD/RWs?
The DVD/RW has an additional annoyance that you cannot drag and drop files to it as easily as you can on a USB memory stick.
So, if I have a 4.7GB DVD/RW, I must re-burn the whole image every time I backup new stuff... with possibly rearranged file/folder structure.
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.
CD/DVD's have a fundamentally different architecture. There are no tracks that can be randomly seeked to. There is just one big spiral track instead.
Since disks are actually pretty cheap per bit these days many are just using "disk farms" for backup. Some are still even using tape.
BUT the DVD has the advantage that you can easily take off site for off-site storage. There's no reason not to use them if they work for you.
From experience, I would never use writeable DVD media for backups due to the high risk of needing the media some time in future only to find out that it's unreadable for some reason or other. Of the two, I'd use flash drives, but given overall choice of removeable media I'd use portable hard disks.
My actual backup technique of choice is to use full/incremental backups to an offsite location - at the home level I have a reciprocal arrangement with a friend and we backup our data to each other's Linux servers using BackupPC, but there are also various 'cloud' ways of doing this for free or a small charge depending on how much storage you need.
Flash memory has a "shelf life" - a period of time after which files on the drive may be lost if the drive isn't used. For cheaper drives, this may be just a couple of months. On the other hand, as long as you're reading and writing it regularly, flash drives can last for years. There is a limitation on the number of read/write cycles a flash drive will tolerate, but I think in virtually all cases the USB connector physically breaks from insertion/removal cycles before the flash storage actually starts to degrade. A DVD can't really be re-used (well, they can be, but they don't have a very long life in terms of read-write cycles), and you can't trust DVD-RWs longer than about a year (which is longer than a flash drive, but still not long enough for deep archiving).
Really, I'd say go with flash drives if you have a small volume of data and you're just keeping "working state" backups from the last few weeks, which is the situation in most environments. If you need to store a lot of data, go with tape (great price per gigabyte) or even a hard disk array (lower price per gigabyte, with the added advantage of much faster access time) like a NAS unit. If you need to hang on to data for a long time, I think tapes still offer the longest shelf life.