The main difference is that an exe is a stand alone executable and a DLL is a collection of functions as they were implemented in LV. That allows you to write a function in LV and call it from another language.
Using either of them will invoke the LV run-time engine (which takes an X amount of memory, depending on the version and the application). Each instance of the LV RTE is limited to a certain amount of memory by the OS (I think the official limit in 32 bit windows in 2GB, but you would probably hit that before). I think that if you open a DLL while running another executable in parallel would open a second instance of the RTE, but I'm not sure.