I was thinking it was the search plugin I was using (Relevanssi), although the plugin author doesn't think it's his problem. I just tried it without the search plugin and I get the same results.
So, with More Types active a search for a word that is in the content of a page and in the title of 2 custom posts shows just the page. When I switch to Ultimate, the same search shows just the 2 custom posts and not the page.
Another example with word in title of regular posts and content of page and custom posts: with More Types I get the regular posts and the page. With Ultimate I get the regular posts and the custom posts, not the page.
I have defined the custom post type the same with both plugins, and set it to be searchable.