I've been Using Joomla since the pre-Joomla 1.5 days, so have seen the arc of development. The current 3.5 version is light years ahead of the 1.5 era, especially in terms of the user experience and upgrades. I am a retired computer database admin, but do not have MySQL or PHP skills. If I was well experienced in those two languages, I might be a lover of Drupal. But without PHP background, Drupal is daunting. So that took it off my plate. I rarely get into the PHP code, though I've dabbled in replacing a line now and then. Mostly, I use and revel in the menuing system, which like Wordpress, lets the entire edifice be managed.
It is worth mentioning that Wordpress is the most popular CMS in the world, at 26.4% of the entire Internet (gazillions of sites), that Joomla is second at 2.6% of the entire Internet (millions of sites), that Drupal is third at 2.2% of the entire Internet (millions of sites),and the rest come in at or under 1%. Wordpress is a blog-specific CMS, while Joomla and Drupal are general purpose CMS's.
If I were upgrading a 1.5 site to a current 3.5 site, it depends on how complex the site is, specifically how many articles. If less than 100, I would do it manually, and copy each article by hand. Larger than that, and I would use a migration tool. Look here:
https://docs.joomla.org/Joomla.... That being said, I have wasted a lot of time on migration tools, and I usually opt for a manual rebuild. Ultimately, it is faster and much cleaner. Think of a Windows "upgrade" vs a Windows "clean install". Similar experience. Easier but clunkier
:).
What I love about Joomla 3.5, over 1.5 is that the upgrade process has gone from ugly to good. In Joomla 3.5, you simply look in two places, the "Joomla Component" to upgrade the Joomla Core, and the "Extensions/Update" manager to upgrade all extensions. To upgrade, simply click the "Upgrade now" button, and "Voila", the upgrades are completed within a few seconds. Light years ahead of the manual processes needed in Joomla 1.5. This means ongoing administration is quick and simple. It is worth mentioning too, that Joomla 3.5 is completely designed to be automatically scalable from Smartphones to Tablets to PC's, where Joomla 1.5 was strictly PC's.
Manually, I would first create an empty 3.5 site. I would then install a current template and try to configure it to look as much like the original as I could. This actually will be the hardest step, and the most artistic. Then I would first create and copy over all the articles and categories as needed, then later the menues. The BEST way to copy articles is to switch to the HTML view, and copy the pure HTML code. Trying to copy the wysiwyg view is never satisfactory. Articles can be copied at the speed of CTRL-C, CTRL-V, which is pretty fast. Then I would create the menu structure and assign the articles and categories, as in the original. Finally, I would examine all the addons, the components, modules and plugins that were added to the original. It will be necessary to find the 3.5 equivalents. Install each one, and configure it as close as you can to the original.
I usually copy the images for the "image" folder lock stock and barrel to the "images" folder on the new site. While Joomla 3.5 does away from the need for the "stories" folder (it was required in Joomla 1.5, not needed but ok in Joomla 3.5), it will still be true that the copied over articles all point to the "images/stories" folder. So unless you want to modify every image link in every article, you can just leave them as they are.
I might add that the two extensions that I always insist on are the JCE editor component and the Akeeba backup component. Both are free, and superb. Good luck however you go.