I just updated to Ubuntu 13.10 and greatly dislike Nautilus 3.8 that comes with it. In Ubuntu 13.04 I used the instructions in this article to get back some of the features from Nautilus 3.4, but unfortunately that doesn't work anymore. I particularly miss dividing up the window with F3 to have two folders show at the same time. The new search function I also find pretty terrible.
I checked out Nemo but I would much prefer downgrading to Nautilus 3.4.
I'm going to risk answering this question since I now feel I have collected enough information on this issue. Basically downgrading to Nautilus 3.4 seems not to be an option at this time; it was coded for an earlier version of GTK, thus it wont compile on Ubuntu 13.10. The only practical way is installing a different file browser.
As it happens, Nemo is actually a fork of Nautilus 3.4 that has kept all the features of the latter (adding a few more). I've been using it since yesterday and the interface is almost the same, a seamless transition for the user. Thus installing Nemo is not very far from downgrading to Nautilus 3.4. I haven't done it yet, but it is possible to set Nemo as the default file browser.
All features I used in Nautilus 3.4 seem to function properly in Nemo (e.g. Connect to Server). The only exception at this stage is the integration with RabbitVCS, there's a package available but non functional at the moment. Since RabbitVCS doesn't work on Nautilus 3.8 either, it is not a regression.
Update II: There's no need to install Cinnamon, just install the Nemo package:
Update I: Nemo's appearance can be tweaked into something closer to the default Unity style. Open its css file:
And then replace all contents with the following: