There are differences not just between airlines but also manufacturers regarding crosswinds. I was a captain for quite a while on the NG and my memory without digging out the manuals was that these were demonstrated not hard limits. There was quite a lot of judgement necessary at times not least because the tower in certain places would report winds that were not always plausible. I used to have the readout on the FMC open with the wind value. We have discussed on other threads why this value is not always to be relied on but combined with the visual picture it can inform judgement. What I would say is that having been to Leeds quite a bit on the 737 you need your best game on days like today.