First let's get into the right mindset about why i'm testing these two Ultra Portable recorders. If you're looking for the best audio recorder for your DSLR, then nothing beats bang for the buck than the Zoom H4n. That's not what this is about. The Zoom H4n is a great device that can support 90% of your audio needs, but there's going to be times when you can't go tethered and things have to be discreet. You'll have to go with a wireless setup and a LAV microphone. When it comes down to 'quality effective' wireless gear, you're looking at $600 dollars a pair. This is what 'this is' about.
These new Ultra portable recorders can act as a nice option instead of using a Wireless setup. For under $150 dollars you can have a truly effective source of audio that is not tethered to the camera operator, very discreet, and less prone to issues that can arise with wireless gear. I'm lovin' these things. Of course, these two products look like they are competitors in the same space and naturally everyone will wonder which way to go. Right now let's just talk strictly 'Form Factor' and size for use as a 'Body Pack'. I'm going to skip to the results and say in my book, Tascam is the clear winner.
They both record the same audio quality, so when used with a LAV microphone and thrown in a pocket, they are equally as effective. The Zoom is the winner for being cheaper, and having a tripod mount, possibly better microphone configuration, and a form factor designed to be used as a handheld microphone. If you're wondering about how you can mount a Tascam on your DSLR rig, a simple Cheap Shotgun Microphone Shock Mount would probably work well, and would be functional to dampen handling noise.
The Tascam DR-08 Portable Digital Audio Recorder is the winner for having a smaller profile which is more comfortable to be used as a 'body pack'. It will fit nicely in a pocket, or throw it into a cell phone case with a belt clip option. The Zoom H1, although can be used in the pocket, loses to the Tascam for this one feature. This is the one feature I'm looking for between these two items. So if your only plan is to use it as a 'body pack w/ LAV mic' go for the Tascam. Again, for the idea to replace a wireless body pack the audio is sufficient. Yes I know it doesn't compare to the Zoom H4n, but try sticking that in your pocket. For you Audiophiles, more audio tests and comparisons will be done soon.
[Update] Here's a video talking about the test, and the RAW files can be found in the links below. If you're wondering why one would be larger than the other, it's mainly because I started one recorder after the other, causing one file to run longer in time. You'll hear a bit of fumbling around as I get things setup, and clap several times for me to sync audio to the video. I did not want to cut, alter, convert, compress any of these files so as to keep things as original as possible for you to listen.
Update: Cheapest price BHPHOTOVIDEO.com: Tascam DR-08 Portable Digital Audio Recorder