CartoDB is great for generating geographic visualizations of data where the geographies are well-defined. It would be great for analysts to develop visualizations of data with spatial elements. That being said, the software is limited if you want to do any real data munging or analysis, as it can be cumbersome to use and there isn't a great interface for actually saving the results of different manipulations (you can save it as a new file, but it's hard to do version control, etc.). I would recommend preparing the data outside of CartoDB and only using the tool for visualization once the data is well prepared.
MapInfo Pro is great for creating and editing spatial data and creating both simple and complex maps. I find it easy to locate tools now that the software has transitioned to a ribbon based toolbar. I also love that you can expand on functionality in MapInfo by adding third party tools as well.
It is amazing at allowing control of the visualizations. It takes a little bit to get used to but the combination of full SQL queries and CSS-like styling is very powerful.
The services are built on a robust stack of open source software. I was able to build a standalone instance of CartoDB relatively easily (after some research and trial and error).
Server side map rendering is key for handling large data sets. The way the images are returned makes them very easy to catch in an HTTP cache to minimize the hits to the server. The interactivity that CartoDB has built in makes this completely transparent to the end user, they can click on parts of the static images and be presented with popups or change map styles. It's a very clever implementation.
MapInfo Pro customer support has always been quick and very helpful with any issues I have had with the software. They usually get back to you about your enquiry within 24 hours and they also tend to follow up to make sure your issue was resolved. I find it refreshing to be able to contact their experts quickly and easily.
I find ArcGIS more comprehensive but with a more confusing interface; however this may be because I learned MapInfo first. Surfer and Global Mapper do more specific things better; but MapInfo is a good overall product for sophisticated GIS
CartoDB definitely saves a lot of time when creating visualizations. Previously, I would use different software and have to make edits manually (or just create the visualizations manually to start with). I would say that the software definitely cuts the time required to create certain visualizations by a half or two-thirds.
