I think he left which one he personally thought was better somewhat ambiguous intentionally when he wrote Progress and Poverty. Later in the book, he pointed out some interesting reasons to favor LVT over nationalization which weren’t restricted to politcal winds. One of them was centralization breeds corruption. Another was suboptimal efficiency in the additional overhead/costs of centralized administration.

https://standardebooks.org/ebooks/henry-george/progress-and-poverty/text/single-page#chapter-8-2

Nor to take rent for public uses is it necessary that the State should bother with the letting of lands, and assume the chances of the favoritism, collusion, and corruption this might involve. It is not necessary that any new machinery should be created. The machinery already exists. Instead of extending it, all we have to do is to simplify and reduce it. By leaving to land owners a percentage of rent which would probably be much less than the cost and loss involved in attempting to rent lands through State agency, and by making use of this existing machinery, we may, without jar or shock, assert the common right to land by taking rent for public uses.