Research the panels used in them. Most TVs use PVA or IPS panels which usually have better color accuracy than cheap monitors (and some expensive gaming ones too) that use TN panels. TN has historically had better response times than IPS/PVA, but that's not a big of a deal these days outside of gaming uses.
The panel type also effects viewing angle and color shift due to off-angle viewing. I'm assuming they are both LCDs and not OLED or Plasma or some other less common tech. If they have different types of panels, color match is almost impossible across the gamut. It can still be impossible with matching panel types depending on the specific models.