If you can stream with VBR but cannot with CBR, that really does hint at an issue with your connection and not at an issue with the software. OBS' netcode is not somehow far more inefficient than XSplit's netcode. Personally i have no experience using Xsplit but I have been around here on obsproject.com long enough to vouch for the massive, massive improvements that have taken place on OBS' netcode.
So... if you cannot stream at CBR <x> bitrate, try going berserk a bit. And go with 50% of <x>. Just to see if you CAN get it to stabilize at CBR. Then, if that is stable, go with 75% of <x>. So, if you tried it at 2000 Kbps CBR, try it at 1000 Kbps first now. If that is stable, try it at 1500. If that is stable, try it at 1750.