AcGFP1 vector can emit light by itself, whereas in case of Luc vector a substrate is needed for the reaction. Nevertheless, Luc is said to be more specific or better than AcGFP1. Why is this so called? What are the advantages of Luc vectors over AcGFP1?
You are confusing luminescence and fluorescence. GFP does not emit light. The abbreviation stands for Green Fluorescent Protein. You need to shine a blue light source at it and it will fluoresce green. The problem is that many organisms have background fluorescence, a cell without any GFP can often have a little bit of fluorescence by itself or contain pigments that mask the signal.
Luciferase assays depend on a chemical reaction which oxidises a molecule (luciferin in the case of firefly luciferase) and photons are emitted. This is much more sensitive than fluorescence but is also a lot more expensive and usually (but not always) requires cell lysis. It is very rare for a cell to emit light by itself so the background will be a lot lower allowing you to see smaller difference.
There are many reasons to choose one over the other in an assay, if you share a bit more on how you intend to use the reporter you can get a more detailed answer.
The vector to use will depend on what you want to do.
The possible problems with GFP are :
The lost of function of the fusion protein (you add 238 amino acids to your protein, that's a rather big change !). There are vectors allowing fusion in C- or N- ter of your protein to try to avoid that.
The GFP may separate from its fusion protein, making observations or immunoprecipitations useless.
With a high expression vector, you may have a saturation of fluorescence in your cells so quantification would be difficult.
With luciferase assay, you add the substrate so your quantifications can be made as soon as the reaction start and luminometers are sensitive enought to detect very low Luc activity or use very few cells.
GFP vectors allows you to do in vivo assays (quantification, intracellular localisation, cell sorting...) while Luc assays needs the lysis of your cells. So, depending of your goal it will be better to use one system or the other.