Dividing the sites into two works out well; our designers are in charge of promoting the marketing site and our developers are in charge of ensuring the web app site is up and functional, which empowers then to focus on their respective strengths. Of course they do go back and forth as needed but for the most part any updates or feature requests are handled efficiently this way.
Our web app does require tighter security, and having the sites split allows us to better control that as well. Any features that our designers want to implement on the marketing site doesn't need to go through as much scrutiny as what we put on our secure web app site. Our web app site requires a user log in, the marketing site does not.
Another benefit in our specific case, we only wanted our marketing site to be picked up by the search engines. Keeping them separate allowed us to effectively hide, for the most part, our user authenticated web app to the general public.
In the rare and hopefully unlikely event that one site may be down, you can also use the other site to post up a status to your users as well.
With using different web technologies, for smaller businesses it's generally a good idea to use the same across the board, that way you only have to look for one kind of developer instead of two when you hire in the future. But if in your specific case you find it makes more sense to keep the technologies different, for example one site is using a pre-built CMS and the other is not, then splitting the site will more efficiently allow you that freedom as well.