unity - Will using a less resource intensive DE on top of Ubuntu be as fast as a distro which uses that DE as default?

I'm asking because I find Unity to be slow on aged hardware which according to the system requirements should work fine (2.53 GHz Celeron, 2 GB RAM). So I want the support of the Ubuntu main release (LTS in my case) but have a more responsive UI using another DE, say Cinnamon or XFCE.

If you install XFCE, your system should be reasonably faster. Even faster if you use LXDE.

I cannot vouch for Cinnamon which I do not have experience with.

It won't be the same thing as using Xubuntu (which uses XFCE) or Lubuntu (LXDE) because Xubuntu and Lubuntu have different packages installed to optimise performance. For example, Xubuntu comes with Thunar file manager instead of Nautilus. Lubuntu contains leafpad as text editor instead of Gedit. Ubuntu and Xubuntu have Thunderbird as mail program while Lubuntu has sylpheed.

This said you should notice a significant improvement on performance because the DE is one of the most resource hungry components of a distribution.

Note that Lubuntu is not available as LTS whereas Xubuntu 12.04 is supported for three years.