question regarding monitors/resolution

Back in the WinXP and prior days, with multiple monitors, you would see a single, very wide desktop resolution.  These days, each monitor maintains its own resolution.  1920x1080 (aka 1080p or FHD) and 2560x1440 (aka 1440p or WQHD) are both currently standard single-monitor resolutions.  I'm guessing the monitors at the two different locations are not the same model?

the monitors are not the same, but I believe the thinking by this particular employee is that it’s a better video card, being 6gig Nvidia, the quality should be way better than the last, where it’s really not that much different.

When you say "way better than the last," what was the last machine's hardware?

All things except resolution being equal between monitors, the only perceptible quality difference between 1080p and 1440p, other than in games and sometimes movies, is increased screen real estate (you can fit more on the screen).  I've found this to be of little use to basic office productivity users, but CAD and graphics designers like it.

In games, images will be a little sharper and, with a mid-tier gaming card like the 1660, it would run pretty smoothly.  You can see some details about GTX 1660 performance vs other cards at 1080p and 1440p here.
https://techgage.com/article/gigabyte-geforce-gtx-1660-1080p-1440p-gaming-performance/2

Regarding just the video card, unless the user is gaming or doing CAD work, they're not going to notice any difference between a GTX 1660 and onboard Intel integrated graphics.

I believe the last computer was a 2gb NVidia - I think the question is, that the other computer he uses at the office is a 4gb NVidia, using dual monitors, where the resolution is 2560x1440, and the NEW computer maxes out at 1920x1080, which in Windows, is the "recommended" resolution, same monitor size. What would be the reason he cant get the 2560x1440 on the new one? Is it the monitor itself? I could have sworn that 2560x1440 was set on the cold computer prior to swapping it out. I can also tell you that the old computer was connected to the monitor via DVI not HDMI. Is this a factor?

>>  What would be the reason he cant get the 2560x1440 on the new one?

Two factors:
  What the card is capable of?
  What the monitor is capable of?

Check the monitors' model numbers on both systems and post them here so we can look up the resolution.

Using DVI it will depend on the cable connection to get 2560x1440 which needs a dual DVI cable, otherwise a standard DVI cable will max out at 1920×1200 (or in this case 1080p).

Hi - sorry for the delay, the monitor with the new computer is a Dell U2712HMT. One thing I can tell you, not sure if this plays a role, but the cable i am using going from monitor to computer is HDMI on the monitor side, and Displayport on the computer/NVidia side. Is there any type of resolution "downgrade" with this?

There can be.  I've seen ultra-wide displays that used HDMI on the monitor side and DIsplayPort on the computer side only do full HD, 1920x1080, but when I replaced the cable with DisplayPort to DisplayPort, the option for 2560x1080 became available.  It's definitely best to not use adapters or different connections on each end, if possible.

ok great - what about HDMI to HDMI? Is one significantly better/different than the other?

Theoretically, you should be able to get 7680 × 4320 (8K) over HDMI, so you'll be fine at the level we're talking about.

It would appear that only HDMI 2.1 is capable of 8k.  However, HDMI 1.4 can do 4K at 30 FPS while DisplayPort can do 4K at 60 FPS.  Again, at 1440p, I don't think it matters.

I found most of this info here:
https://www.cnet.com/news/hdmi-vs-displayport-vs-dvi-vs-vga-which-connection-to-choose