Okay, using the
ballistic calculator in WWII Equipment:
Centurion I vs 88mm KwK 36 firing late war
APCBC...at the turret (left) and hull (right):
Red equals high chance of pnetration, orange means penetration is possible but unlikely, yellow means the shell may shatter on impact and green means you'd be bloody (un)lucky to get a shell through...
So, in the simplest approximation (gun+ armour =?) a Tiger I could reliably kill a Centurion I from the flanks or rear at all ranges, but would need to be at point blank range to get through the glacis. At a range of around 1200m it'd have a good chance of putting a shell through the front of the turret (I suspect the calculator is only working on the 'mean' armour thickness over the front of the turret, not including any additional mantlet armour). Using an
APCR round for the KwK36 leaves a Centurion's turret vulnerable at all ranges and angles out to 2km, but is still unable to get through the Cent's frontal hull armour.
The King Tiger's KwK43 can kill the get through the Cent's turret at all ranges and angles, but may have trouble agains thte hull from front-on beyond 1700m
Putting the boot on the other foot and using a 17 pounder to pop bog-standard AP at a Tiger I (turret, left, hull right):
So, even with a bog standard AP round the 17 Pounder should be able to get through a Tiger's hull armour out to 2km from front, flank and rear. For the turret, a chance of getting through the front out to 1900m with a good chance within about 1600m, with the proviso that this is based on the 120mm thickness of most of the Tiger's turret front, not the 200mm of it's mantlet, flanks and rear are predicatly enough easy. Trying again with 17 Pounder APCBC and
APDS and the Tiger I's dead at pretty much any angle out to 2000m.
Repreating with 17 pounder vs Tiger II... vulnerable to plain AP and APCBC on flanks and rear at most ranges, only vulnerable front on at point blank. Hull invulnerable to APDS from front on, but turret vulnerable out to 2km.
EDIT: NOTE THAT THESE ARE VERY GENERAL FIGURES AND ANALYSIS... DO NOT TAKE THEM AS A FIRM ANSWER TO IS "X BETTER THAN Y?"