Generally speaking, there should be little difference between an analog signal and a digital signal. An analog signal is basically a converted digital signal, so there is always a possibility of some signal degradation.
There is a difference between watching a movie on an IPS panel vs. a TN panel. TN panels use dithering technology to generate 16.7m colors from only 256k actual colors. This can create artifacts on the screen; either color banding issues with color gradients or general pixellation that are not actually in the source material.
Inexpensive IPS monitors use the e-IPS which almost all use 6-bit color technology just like all TN panels monitors. There is only one or two 8-bit e-IPS panels manufactured and only a very few monitor models actually use them. These 6-bit e-IPS panels can also show some color banding issues and general pixellation, but not as much or as glaring as TN panels.
For the cleanest signal you want to use DVI, but it may be hard to spot any differences. The biggest difference would be in using different monitors, not different connections, resolution and cable quality and length being the same. I went from a cheaper screen on DVI to a nice IPS screen with the same cable and video card, and it was a huge difference. Felt like I upgraded my whole PC.