In Rogue One Blue Squadron got through before the shield closed and managed to blow up AT-ATs but in The Empire Strikes Back they have to use cables to bring them down. Why?
They were not AT-ATs but AT-ACTs (all terrain armoured cargo transports). Wookieepedia link
They are larger than AT-ATs but have no armour covering their centre which is open and used to transport cargo.
Have yet to see a vehicle cross section on this one but AT-ATs used heavy blast resistant armour plating making blasters all but useless against them (in old canon the snow speeder blasters were more powerful than what was found on x-wings) since these were cargo transports it could just be normal armour plating.
Also in old legends canon the ESB ATAT was still under construction and testing during this time with the battle of hoth being its first official battlefield test.
The T-47 airspeeder was very much a jury-rigged combat vehicle. It was designed by the Incom corporation as an industrial cargo-handler, and was later modified by the Alliance with weaponry. If we were to find a modern-day analogy, it would be something like a so-called "Technical" - a pick-up truck with a gun mounted in the back. A vehicle like this is fine for patrolling and anti-infantry work, effective against light armour like an AT-ST, but it was totally outclassed by a heavily armoured combat vehicle like the AT-AT.
The T-65 X-Wing is a totally different beast. It was a purpose-built starfighter, designed to attack armoured targets and blow the living, ah...daylights...out of them, and had sufficient shielding to survive attack runs on defended targets. The closest comparison would be something like the F/A-18 Hornet, which is designed to fight its way to a target, hit the target, and fight its way back out again.
In fact, the X-Wing was originally being designed for the Empire, as a more powerful complement to its fragile TIE fighters. At the end of development, however, the entire Incom corporation defected to the Rebel Alliance, taking all the designs and prototypes for the X-Wing with them.
The X-Wings and other fighter craft taking part in the battle on Scarif in Rogue One have more powerful weapons available to them than the blasters on the snowspeeders used during the Battle of Hoth.
Even if the X-Wing blasters aren't enough on their own, they've got their missiles/torpedoes.
In the Battle of Hoth a walker is shown being blown up by blaster fire after having been weakened by other damage first.
Essentialy, both crews used the most suitable weaponry they had available.
In the ESB, movie portraits mainly the T-47 airspeeders, armed only with double laser cannons. On the other hand, they did have the harpoon gun, which they brilliantly used against the walkers.
On the other hand, X-Wings were one of the best starfighters in Alliance arsenal, very verstaile, and equipped with 4 cannons, as well as proton torpedoes launchers. Most of the X-Wings also used astrodroids, who help a great deal with piloting and aiming. Thus, better aim and better weaponry = more destruction. (And they didn't have the harpoon gun, so they had to bring the walkers down with sheer power.)