This pages tries to explain differences between CRIU and other C/R solutions.
DMTCP
DMTCP implements checkpoint/restore of a process on a library level. This means, that if you want to C/R some application you should launch one with DMTCP library (dynamically) linked from the very beginning. When launched like this, the DMTCP library intercepts a certain amount of library calls from the application, builds a shadow data-base of information about process' internals and bypasses the request further, to glibc/kernel. This information will be later used to create an image of the application. With this approach, one can only dump applications, that are known to run successfully with the DMTCP libraries, but the latter doesn't provide proxies for all kernel APIs (for example, inotifies are known not to be supported). Another implication of this approach is potential performance issues that arise due to proxying of requests.
Restoration of process set is also tricky, as it frequently requires restoring an object with the predefined ID and kernel is known to provide no APIs for several of them. For example, kernel cannot fork a process with the desired PID. To address that, DMTCP fools a process, by intercepting the getpid() library call and providing fake PID value to the application. Such behavior is very dangerous, as application might see wrong files in the /proc filesystem if it will try to access one via its PID.
CRIU, on the other hand, doesn't require any libraries to be pre-loaded on the application start. It will dump any application. But to do so, CRIU requires a certain information to be fetched from kernel, and if it can't be done, the respective patch is submitted to the kernel community. This means, that CRIU supports all the features only on the recent kernel. However, this is temporary situation. One day kernel API will be extended to the necessary level.