I'll be honest, I don't know Google Earth Pro at all really. However, I know ArcGIS Explorer Desktop. It is a very useful program for me and my organization. It has a relatively wide variety of capabilities compared to at least what I'd expect for a free program from a commercial software company like ESRI. It can consume a wide variety of GIS datasets and, if you are comfortable with their APIs there is the potential for you to build a wide variety of customized plug-ins for it. Even without coding, they have a nice administrative side built in that lets you configure toolbar layouts, options/tools/functionality available to each user, program defaults, and other application customizations that can be configured to give different users different access to various tools and/or make the program even easier to use by limiting unneeded functionality from the interface.
Above and beyond all that though, personally one of the most useful abilities of Explorer to me and my org is it's ability to read directly from SDE database/file geodatabases using standard ArcMap generated layer files. I have gone in and set up a number of layer files in ArcMap, some using definition queries, some using rather complex labeling configurations, etc... and all I do is save out those layer files and the users have access to that data live from the layer file's data-source.
Also, explorer can consume ArcGIS Tools published as services on an ArcGIS server. This is somewhat of a limitation in that, without you coding your own plugins, I don't know of a way for it to perform complex analysis without server based GP tools, but there is the fact that it has the ability to do complex analysis at all....
Also, when having a similar conversation previously with various people, it has been repeatedly been brought up to me about a feature limit they thought existed in ArcGIS Explorer. It seems from what I can gather that maybe some original versions of ArcGIS Explorer had a limit of 10,00 on the number of features from any dataset that could be displayed, but this is not a limitation as far as I can tell anymore. I've had multiple datasets, each with 50,000+ features, all displaying correctly, at the same time, in ArcGIS Explorer Desktop.
On the other hand, some of the limitations I've found are:
A) It can supposedly consume arcgis geocoders/geolocators but I've never read of anyone actually being able to successfully implement this functionality, and indeed I've tried myself with no success. It does have a default, built in, locator service functionality where you just type in an address in the search bar, but if you're trying to use the advertised "consumes customized local geocoders" functionality, good luck.
B) It has a lot of functionality, but without going through the administrative application management configuration steps, the sheer volume of options and tools/buttons available to the user can be a bit intimidating for some techno-phobic users.
C) Without using a geoprocessing service or a custom-built plug-in, I don't know of any way to allow ArcGIS Explorer to edit data in an existing database. Now, that being said, the program easily lets you create new data within the program in the form of point, line, polygon, and even more or less annotation style "notes". Also, if created within the program, you can edit them within the program and you are able to share any of these out of the program as Layer Packages that could be opened and edited/interacted with within ArcMap. But understand that connections with existing data, ex: layer package reading data from ArcSDE, are read-only connections. Any editing other than the above mentioned exceptions would have to be notes created within the ArcGIS Explorer program and shared with ArcMap users who would review those notes and actually execute any noted changes that needed to be made.
There are other aspects to the program as well, I know there are, but that's at least the feedback from the parts of the program I know decently well.
Also, final note, remember with ESRI you get what you pay for. If you go the route of ArcGIS Explorer be ready to jump on the ESRI forums and/or this site with questions because it is not a program with ESRI support (however, I have on occasion had issues of getting data from ArcMap moved over to show up in ArcGIS Explorer how I wanted it and ESRI support has been able and willing to assist me with this as an ArcMap support function).