There are many differences between these two products. Definitely the NUC will be powerful and faster than the Pentium processor E5500.
Here is the comparison chart:
Would the Lenovo with the I5-3470T be the fastest? That would be the simplest "all in one" to replace the old setup and at the price I might be able to get it for would be the cheapest solution.
I am not sure about the brand/specifications of the computer but I can tell you the I5-3470T is faster than the Pentium processor.