XLR can ground the hot tip when plugging in, while TRS won't. Else both same three conductor balanced cords, afaik. Edit IMO, XLR are sturdier. Polar pretty much nailed it. I prefer XLR for exactly ...

You actually want the stereo signal split into two separate monos, since balanced is a mono connection (ground, positive signal, negative signal). Most likely the reason this didn't work is because ...