You asked people what they thought was nice, among the various QG proposals/attempts. Just saying "string" or "loop" does not tell us much. You have to refer to a specific paper that defines what they are talking about. At least for LQG there are several recent papers describing new versions. of the theory. Bahr Dittrich Geiller being just one of 3 or so.
What I think is nice is when a QG theory predicts a cosmological rebound---instead of a singularity---and makes predictions that can be tested.
So it should reproduce standard LambdaCDM cosmology starting soon after expansion gets started. possibly dispense with the need for inflation (which has a lot of problems), and as you go back in time to the start of expansion you should not encounter a theory failure (a "singularity" i.e.. breakdowm/blow-up) but rather a collapsing phase that rebounds at high density. Quite a few models do that now.
Since you wanted to know, the kind of QG paper that intrigues me most is like this. It gets rid of the singularity and it predicts the right stuff (agrees with observations so far) and it gets rid of the need for inflation (which is kind of contrived and has problems).
http://arxiv.org/abs/1412.2914
A ΛCDM bounce scenario
Yi-Fu Cai,
Edward Wilson-Ewing
(Submitted on 9 Dec 2014 (
v1), last revised 28 Jan 2015 (this version, v2))
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. ..
...
... We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly
scale-invariant.
...
...Importantly, as this scenario predicts a positive running of the scalar index,
observations can potentially differentiate between it and inflationary models. Finally, for a small sound speed of cold dark matter, this scenario predicts a
small tensor-to-scalar ratio.
14 pages, 8 figures.
===============
This is the first hit if you simply google "LambdaCDM bounce"
LambdaCDM is the standard model cosmos that all the cosmologists are using. These people added a bounce and found agreement with observations (I highlighted some) and testability versus inflationary models. And they got rid of the singularity and the need to cook up an inflation episode.
That's the kind of QG thing I think is cool.