Does a short barrel or a long barrel kick harder?

The longer the barrel the more time the powder has to fully burn inside the barrel, which in turn increases the pressure inside the barrel and the muzzle velocity of the bullet. This generally results in greater recoil. (though not necessarily greater "kick") Though other factors must be considered as well.

For many small caliber rounds like the .17 and .22 you're not going to see any noticeable increase in recoil going from a 18" to 22" barrel.

Another much greater factor is the ammunition. Cheaper ammunition, such as typical store brought ammunition, has a less powerful powder or simply less powder all together than brands or custom loads. Lets take a .308 for example. A .308 cheap bullet isn't going to have any noticeable difference going from a 20" barrel to a 24" barrel. However, change the ammunition to (just for a good example) Double Tap Ammunition, and now there is more likely to be a noticeable difference from even a 22" to 24" barrel.

Next up is the grain of the bullet itself. A heavier grain is going to generally have more recoil. (the heavier the bullet.. the harder it is to move.. the more energy from the expansion of gasses is transferred back into your shoulder.)

Another important factor is the action of the gun. Bolt, sing-shot, break-over, pump, etc. have greater recoil than auto / semi-auto (gas or mechanical). since none of the energy is being absorbed to chamber the next round. (Also with gas operated barrels the size of the gas port can also change the recoil of the weapon, though typically not enough to be noticeable)

Now lets get back into the question. Does a short barrel or long barrel kick harder. The energy being transferred back into your shoulder is generally greater the longer the barrel, but often feels less 'instant' and more as a shove.

EXCEPTION! - In general, a longer bull barrel will have less recoil than a shorter standard hunting barrel, since the bull barrel weighs more. (heavier the gun the more energy required to move the gun the less recoil)