NikonJohn Loc: Indiana U.S.A.

Not sure if this is your issue, but this is what was happening to me with that same result.
I was having prints made rather than using my printer though, but I would think the issue might be the same.
First, are you printing/working from jpg or raw files?
I was printing from TIF files (made from raw files), because there is no color compression with TIF's and this was the problem I had a number of years ago. I had set my camera to Adobe RGB rather than sRGB because Adobe RGB has a larger color pallet, so I thought that would be better. However if the lab (but maybe printer also) does not pay for the Adobe license they don't have that color pallet, so in my case they just printed from the sRGB pallet without converting. This was making the colors in the prints really dull looking. I have since set my cameras to sRGB and I don't have the problem any more. I can't imagine there is a huge advantage to the Adobe color pallet even if it is bigger... my prints from Nations Photo Lab look great from sRGB tif files. They don't look quite as good if I send jpg files (I did that once for a calendar). If you are using Adobe software and shot it Adobe RGB it may be sending the Adobe colors to the printer and the printer may not recognize that color pallet. Check your cameras color pallet settings and see what they are. If it's set to Adobe RGB change it to sRGB. When you are working on the computer save the files for printing as TIF files. Then send the TIF file to the printer and see how that looks, they look great on my HP printer. This might be worth a checking into.
Hope you find the issue soon, ink is expensive.

Rich1939 Loc: Pike County Penna.

This morning I ran off 4 test prints. 2 were 16 bit and 2 were 8 bit. Of each bit pair 1 one was printed with Photoshop in control and the other with the printer in control. The 16 bit images were left in Adobe RGB while the 8 bit were converted to sRGB.
After letting the prints dry down the 4 of them were shuffled and then I tried to determine by looking at them which was which.
I couldn’t see much, if any difference from one to the other. Maybe the PS controlled prints have a tad more contrast, but I wouldn’t bet on it.

All this means? Does the printer's software compress the input colors to match its color space so that it doesn't matter to any large degree what color space and bit level we input with??

If it matters, I print with an Epson R3000

cjc2 Loc: Hellertown PA

Nice try at Hijacking the thread! To answer your question you'll need to provide a lot more information such as if you have a calibrated workflow, paper, ink, icc profile, etc.. If your question is "Is there a difference between software control?", then the answer is yes. Printing photos involves a lot more than just hooking up your printer. Check the Red River Paper site for detailed information. Best of luck.

Rich1939 Loc: Pike County Penna.

I'm happy to see that you appreciate my effort to address something that was brought up in this thread. To wit: what effect various conditions could have on the final print.
You know from previous posts that I have a calibrated set up and that I have read the Red River information. If you don't agree with what I found, explain why.
BTW Since I used one image and only varied the printing control method, bit depth and color space for this test if my monitor is calibrated (it is) or not, would have no bearing on the results since I never touched any adjustments during the test.

Your unwarranted attack from out of left field has been entertaining. I await further light moments.

The Watcher

I suggest visiting this site and looking through the playlists, I'm sure you find some answers there.

https://www.youtube.com/channel/UCz9YXaSulpM90vC24lmAeZA

SuperflyTNT Loc: Manassas VA

It has nothing to do with the lab not wanting to pay for Adobe RGB colorspace. It is a physical limitation of the printers, even sRGB is a wider gamut than the printers can accurately represent. There is also no advantage to sending a TIF over a JPEG. This might not be true if you're sending your work to a high-end lab, but even then it's hit or miss. Also a good inkjet printer might support a wider gamut like Adobe RGB and even possibly ProPhoto RGB.

Golden Rule Loc: Washington State

Yep. Always check for driver updates and paper is correct side and type according to ICC profile.

anotherview Loc: California

I believe the recommended approach is to let the software control the output.

I've never done it, but you can set a printer profile for each paper.