Since people are asking every week, I made a quick comparison!
1) Outdoor Environments
The biggest strenghts of Cryengine are the dynamic lights, vegetation and shadows. The day/night cycle works really nice in outdoor environments. The problem is the indoor environments, since Cryengine only supports one UV channel you have to bake your AO into the textures, which makes it hard to mix an AO/shadow map with tiled textures (or simply baking the lighting globally as in UDK), the result is that you have to fake the indoor lighting with dynamic lights. This means that when you could just bake a realistic light setup, you have to do it manually, with lights, spotlights and cubemaps, and this is hard and takes alot of time. Dynamic lights and day/night cycle is in the end not useful, since you are using these features to manually fake lighting, you cannot later change the time of day, since your cubemaps and lights that are placed for daylight will break the illusion of night time.
2) You are modding Crysis
If you do not have a company with employees and money to develop, you will be working with FreeSDK, which is nothing else than Crysis without the cool effects, guns, tanks and enemies. So you can just as well mod Crysis, since they will both be free games. The resources that come with FreeSDK really sucks, and that is intentional to force you to make your own, nothing wrong with that, but you could do the same with Crysis, and maybe use one or two of the explosions already available.
3) Disillusioned Community
There is little sharing of resources on the Cryengine community Crydev, and little activity, nothing available really to learn from and its members are becoming disillusioned by the neglect of the community from Cryteks side.
1) Sharing: The community and resources
On Blenderartists.org, blendernation, blendswap, blender3darchitect etc. there is all the resources and tutorials you need to learn. And resources for you to make your video/game/presentation. You can literally begin stitching together different features that people share in the community and learn that way, the best way!
2) Baking, textures and 2d filters
BGE does not have the dynamic lights, daycycle and nice shadows as CE3. The features exists, but are not as optimized. A day/night cycle would be possible with the Preethams sky shader, and some python to control the energy and color of lights, but you would need a nicer sun shadow feature, that would give you different shadow resolution per distance and a nice fading at the end, I haven’t seen this as of now, and finally we need to wait for the Harmony phase 2 for faster dynamic lights. In BGE at the moment you need to use some tricks. You need to bake lights, use python shaders and 2d filters to get a nice look!
3) Unfinished features
The biggest problem with BGE is that there are many cool features that are either in pototype stage, or unfinished. For example the Box Projected Cube Mapping technique is awesome, but has not been integrated into blender, and I have not yet seen anyone improving the code so you could more easily set it up. Recently CE3 integrated BPCEM, as a object that you place in your scene, set the size of the box and press “generate cubemap”, and that is it! Alot of features available here could easily be improved and integrated into blender, and mostly this is what Candy branch is about, but it is moving along slowly. And also, in my opinion, the biggest problem with BGE is that the 2dfilters fry my GPU, they need optimization!
CE3 FreeSDK is nothing else than a stripped down Crysis version, for making free games you are better off using Crysis / Crysis 2 mod SDK.
BGE has more limitations than CE3, but you have more control. When it comes to scenes and environments, you still have to fake lights in CE3, unless you are doing outdoor environments, like a forest. But indoor environments are harder to setup placing dynamic lights in CE3 than just baking textures in BGE.
If you want to do a free first person shooter, with an outdoor setting, use CE3.
If you want to do a commercial game, or a free game with any other setting, or not a first person shooter, use BGE.
My Creydev thread: http://www.crydev.net/viewtopic.php?f=309&t=79981