Just looking at damage progression for PAthfinder vs 13th age. Only looked at a few martial characters so far.
13th age is easier to do due to lesser amount of options. Roughly, Using Rage a barbarian will take 3 rounds to kill an equivalent monster at L1 an d L5, and 4 rounds at Level 4.
A Rogue using sneak attack will take 4 rounds at L1, L5 and L 10. As will a Ranger with an animal companion.
Because characters damage accelerates with level, fights shouldn't take any longer as you level up.
For Pathfinder i've only looked at the barbarian so far.
Versus a standard L1 monster, a L1 Str 18 Barbarian using Large great axe, power attack and raging averages 8.25 damage per round (average roll x % chance to hit AC) which would 2 rounds to kill. So quicker than 13th age without using minions.
However, once i start going up levels this drops off. Partly because AC goes up quicker than BAB, but mostly because HP goes up every level and damage does not.
At L10, using Vital strike, PA, Rage, i can average 18 per round (average damage of 40 x 45% hit) or do 2 attacks but then i drop to 15 per round due to lesser chance of 2nd attack. This would take 14 rounds to kill an average L10 monster with 130 Hp. See HP is x 10, but damage is only doubled.
Should have done L11 because then VS does x3 damage.
At L20, again using VS, PA, Rage i do 33.75 per round (70 x 45%)! but now the HP is upto 370 so i take 11 rounds. From L1 the damage is 30 times bigger, but my damage output is only about 4 times bigger.
Now i haven't used any magic items (because i didn't for my 13th age stuff either) but there is still a problem here.
Sure i could throw in some casters but they have single use spells.
What is the solution? I do not see any conclusion other than combats take longer as you level up because enemy HP is going up massively and your damage is not. You then get extra attacks, but the BAB is so low they can't hit, and feats like VS only give you increases of x2/x3/x4 when at same levels enemy hitpoint is x10/x20/x30.
Is this a standard flaw of Pathfinder or have i got something wrong? I haven't played to these high levels, i'm just doing the numbers. But having played a few sessions of 13th age and being able to throw 100hp monsters at L2 (L4 in PF) characters and them killing it in 3 turns, i'd like similarly quick fights in pathfinder...well maybe not that quick!