Debian Testing
Debian Testing is an unstable, rolling release in which things are likely to break, but you get pretty continual access to new versions. Unfortunately, of the three Debian distributions Testing is the most poorly supported with regards to security.
Debian Testing is very similar to Debian Unstable with the exception that version updates reach Testing at a later stage, or not at all if they have too many release-critical bugs.
Due to the continual updates and changes to your system when using Debian Testing, I'd recommend only using it if you are only using it on your own PC and you don't mind spending a fair bit of time updating things, changing configuration when something changes, etc. I'd also recommend running a mixed Testing/Unstable system because when Testing does get a serious bug, even though it will happen less frequently than in Unstable, it can often take a longish time for bug fixes to reach Testing because they might be held back due to a host of reasons.
If you require any form of Stability, or you are maintaining a server, multiple desktops or a computer for someone else who is less of a 'superuser', by all means stay with Debian Stable. Remember, even though it's older, you can backport to it.
Ubuntu Stable
An Ubuntu Stable release is a stable release made every 6 months from a snapshot of the Debian Unstable or Debian Testing branch. It goes through a cycle of bug fixing where it is effectively 'frozen' for a time being and Ubuntu-specific changes are applied to the otherwise vanilla Debian snapshot, then it is released.
Being a Stable distribution, an Ubuntu Stable release doesn't get new software at all, except when you upgrade to the next release. The releases are 6 months apart, plus there is the freeze period for however many months, so adding those together is how far behind you'll be from Debian Testing or Unstable in terms of software versions. Debian Testing on the other hand is getting new software releases all the time, many in as little as 10 days after they are released upstream, and it'll take months for that to filter down to an Ubuntu stable release.
Ubuntu LTS
Ubuntu LTS (long term support) releases are managed in pretty much the same way as Debian Stable releases, apart from the philosophical differences and Ubuntu-specific bits that Ubuntu adds. Here you'll get even more stability, that is, new software versions will be even less frequent, with a new version available only every two years, again same as Debian Stable. But if you are managing a server or a number of desktops, or managing a desktop for someone else that is not a superuser, then you will save yourself so many headaches by going with Debian Stable (or the similar Ubuntu LTS, though I prefer Debian) and not having to update stuff all the time.
My personal experience
I have used Debian Testing (pulling in some packages from Unstable when absolutely necessary) for quite some time now (over 9 months) and dissatisfied with the instability of the release. When it was new to me, I liked it fine because the novelty had not worn off, but having to download tens of megabytes of updates every day that I use it gets old. I've been through kernel upgrades, and Xorg upgrades, and each time something like that is upgraded there are things which stop working or which need to be reconfigured because the new version does things slightly differently. The recent new Xorg changed the way my touchpad behaved by default, and it took me ages to set it up again so tapping to click worked, by default, in all user accounts. It's just things like this that keep on changing. Uswsusp stopped working, making hibernation completely fail, and it still isn't fixed in Testing. A recent update to enable kernel modesetting for Intel cards completely hosed my system, making it near unusable, and I have had to manually set modeset=0 in my modprobe configuration for now.
I love that it has new software, but I want to move to Stable now and stop all this constant changing. I've been telling myself I'll wait until Debian Squeeze and then stay with Stable, but it's annoying me so much now I'm thinking of downgrading or reinstalling to Lenny. Lenny is well supported, and if you want new software there are tons of backports for it letting you run newer software on it without having to compile or install it manually.