The result was wonderful. Of course, there are many mistakes that can be made. I decided to read the documentation very carefully, step by step, while I did the migration. The comments about using Akeeba backup for the 1.5 original site need very careful scrutiny of the Akeeba site to make sure that there is a version compatible with your combination of Joomla and PHP - and there may not be. I skipped all of that and used cPanel for the backup.
The basic upgrade worked like a dream. I made one mistake - I also copied over the templates - that was a mistake. I deleted the first jupgrade migration and re-ran it without the templates (yes, that left me a bit uncertain about comments suggesting jupgrade can damage the 1.5 installation - I had no problems, after the upgrade, accessing the 1.5 and 2.5.6 sites before switching them over, and no problems running jupgrade a second time on the 1.5 site). After the 2nd upgrade without templates, I reinstalled a 2.5 compatible version of the template. It took more time configuring the 2.5 compatible version of the template than migrating Joomla with jupgrade.
So, for me, it was an extremely helpful tool. My bottom line is follow the documentation carefully, step-by-step, backup with cPanel or something else, rather than Akeeba (I installed Akeeba backup and admin tools after the migration) unless you are certain you have a compatible version. If you have a 2.5 compatible version of your template, don't try to migrate the version 1.5 template; install the 2.5 version after the migration the configure the template.
Great tool - so good, that it left me very puzzled about some of the negative reviews here, but I guess some people had big problems for some reason or another. I'm really pleased I decided to try it.