The final result depends therefore on the cosmological model on which our estimates are based. On the contrary. HST results have been very spectacular, as well as the follow up from the ground. However, a small number of objects and a very small volume of the universe has been investigated. I think that the large telescopes from the ground will provide excellent data on larger samples that will allow us to establish how general the HST findings are.
Astronomy needs large samples to derive statistically significant results.
Besides that, there are many fields of astronomy that will benefit from the large telescopes, like galactic structure studies, which will help us understand more deeply many properties of galaxies in general. The interferometric capabilities of the new telescopes have not been exploited yet. For sure they will provide enormous amounts of valuable new information. Population synthesis models have been crucial in the development and success of photometric redshifts techniques. The uncertainties arise once we want to interpret the spectrum of a given galaxy in terms of its stellar population content.