First, both eglibc and uClibc were developed with the intention of having a small footprint and thus to be suitable for use in embedded devices. glibc is a huge library that wasn't well suited for that purpose. Yet, those two libraries differ in a way they try to achieve that purpose.
eglibc
eglibc, or embedded glibc, was developed with the intention of being source and binary compatible with glibc. That means that isn't necessary to recompile existing binary applications compiled for glibc in order to be possible to run them on eglibc. On the other hand, since it is source compatible with glibc, that means it is possible to recompile the source without any modifications. Yet, according to FAQ on eglibc page, eglibc development is stopped, and all embedded development will be done directly in glibc tree. This was announced on July 20th, 2013. That also means that almost all patches from eglibc will be ported to glibc. You can find more information here about the patches that are not going to be ported back.
What might confuse is that the newest eglibc release is based on glibc 2.19 which was released in April, 2014, a year after announcement that eglibc development will stop. But, this is according to the plan of phasing out separate eglibc tree. Also according to the plan, this is a last branch. All the branches will be maintained as long as the base glibc versions are maintained.
In June 2014 Debian announced that it's going to switch back from eglibc to glibc due to the changes in the governing structure of GLibc project. The reason for the change is that Ulrich Drepper left RedHat.
uClibc
uClibc, on the other hand, was developed with the intention to be source compatible only, i.e. no binary compatibility and thus binary programs compiled for glibc (or eglibc) have to be recompiled. uClibc is actively maintained even though the latest release is from 2012.
Conclusion
So, what is the conclusion? The conclusion is that if you don't need to be binary compatible, you should use uClibc on OpenWRT. After all, all the binary packages on OpenWRT's site were compiled against that library. If binary compatibility is important to you, then glibc is the way to go. Unfortunately, since in OpenWRT there is eglibc and not glibc, you have to go eglibc route. Note that this also means you'll have to recompile all the sources for OpenWRT since you'll not be able to use precompiled binary packages!