This new update addresses some security concerns, among other things. From what I can gather the majority of Leopard users are having good success with the upgrade. However, there are a fair number of users who are experiencing a number of issues. According to the Apple support forums many people are getting the upgrade installed OK, but others seem to be having problems runing the gamut from issues with wireless devices to problems with iLife programs. There are also reports of issues with the download as a part of the Apple Software Update process and trouble rebooting the Mac after the install.
The best advice at this time is to use the combo update (http://support.apple.com/
When I did the upgrade on the Mac Mini I followed some advice that I had received on the Apple forums. I did a disk permissions repair (using the Disk Utility found in Finder->Utilities) before I started. After that I just installed the upgrade and it worked OK and so far I've not had any issues. But it is a very plain vanilla setup.
I decided to do my iMac next. This time I did it a little differently, again with information gleaned from the Apple forums. I did the disk permissions repair first, but before I installed the combo update, I rebooted my iMac into Safe Mode (http://support.apple.com/
One person on the Apple forums noted that his install had the negative consequence of considerably slowing down his Airport connection. I had immediately checked to make sure that I still had wireless access to the Internet, but had not bothered to check the speed. I logged onto a speed test site (www.speedtest.net) and checked the speed which seemed OK. But I didn't have a benchmark to compare against. So, I wirelessly hooked up my other iMac that still was running 10.5.6 to my Airport base station and ran the speed test on it and I got almost the exact same results.
I lastly did my personal iMac upgrade using the combo update, but without going into safe mode and without checking permissions and it seems to have worked OK as well.
I have not tested doing the upgrade through the software update process. However, the consensus on the Apple support forum seems to be that the combo update is the way to go. It's only slightly more hassle than doing it through the software update and I am going to make that my standard way to do point release in the future.