Most of the relevant points have been made.
The last time I checked, lightjet prints here in Oz were cheaper than inkjet.
The lack of richness/shadow depth and saturation in some inkjets is usually due to bad profiles.
There are a lot of these around. With the larger gamut of inkjet and the sheer density of 8-12 pigments laid down, compared with 3 dyes produced in lightjet, the potential of much richer inkjets can be reached with properly crafted profiles and the laying down of sufficient ink. Some suppliers cut costs by running printers faster or at lower resolutions that weaken the print. This is more difficult with lightjet.
The 9600 printer you mention is an older generation machine. It's inkset suffered from colour inconstancy and low DMax on photo type papers. It's inks took quite a while to stabilize , so getting colour right was difficult.
If you find a printing service using current inkjet printers, running at high resolution with good custom profiles, I think you will find the results more satisfying than inkjet, but you may have to pay a little more. On the other hand, lightjet are more robust and have a "look" that is somewhat more traditional which often suits reference sheets, mass production ( like postcards) , student folios and medium term display prints. I think inkjet has it for fine art.