I don't spot an answer to this question, so thought to re-post it here. Larger airplanes are heavier and would ostensibly be pushed less by the wind compared to a small airplane? Do larger airplanes have higher crosswind limits then?
Generally yes, since a 20kt crosswind requires considerably less crab angle on final at 135kt compared to 70kt. The CRJ900 has a demonstrated max crosswind component of 32 kt (If I had those conditions in a 172 and had to put it down, I think I'd just land across the runway).
There is also a significant technique difference once you get above, say, 100,000 lbs, or depending on the engine location. On heavies where you only have a few degrees of banking margin when the gears touch before the nacelles hit, the technique is to fly wings level crabbing into wind into the flare, and give a large boot of rudder just prior to touchdown, and get it down before you start drifting off to the side (you are effectively in a skidding turn, but there is a delay before you start to actually change direction and you have to achieve ground contact in that delay period, so you make it snappy and don't work on teasing out a smooth touchdown).
On smaller aircraft it's more the traditional sideslip technique, wing low with opposite rudder maintained to keep runway alignment through the flare and touchdown. My jet time was on CRJs and I would land in crosswinds slightly wing low with rudder to keep aligned, similar to landing a glider in a crosswind (it took about 7-9 deg of bank to risk tip contact and a crosswind would never need much more than 3-5, although tip strikes do happen in the CRJ fleet from time to time when pilots have an oops on landing).
Transport airplanes generally don't have a maximum crosswind component as a published limitation, but will list a "demonstrated" crosswind component with the statement "not considered limiting". It means that it's only the maximum component demonstrated in testing, and you are free to land in stronger ones, but the manufacturer doesn't vouch for the ability of the plane to handle it.