All applications use different color management in displaying their image to a computer screen. This will also vary, depending on how the display's color profile is set. You will never find consistent results between different applications when judging on a computer display. It will also vary a bit based on the codec used.
If color is really critical to your project, you should make judgements based on using an I/O hardware device (BMD or AJA) and viewing your output on a high-quality broadcast display. I realize that's a frustrating answer, especially if your delivery is only for the web, but unfortunately that's the nature of the beast.