The way PC's in 4th edition start out with more HP and powers and the sheer fact that 4th edition was geared more towards a "heroic" type of PC than the farmer's son having wonder lust shows how it is more than just the DM.
Well, it looks as if 5e PCs will still start out with more hit points and abilities than average, but it's probably closer to the 3e level of more.
For example, compare a 1st-level human fighter with the human commoner in the bestiary.
The fighter has much better ability scores (16, 15, 14, 13, 11, 9, an additional +1 to any score for being human, and an additional +1 to Str, Dex or Con for being a fighter compared to 10 across the board).
The fighter has much better hit points (10 + Con mod, compared to 4).
The fighter has a +3 bonus to weapon attacks (and it will likely be higher because of positive Strength and Dexterity modifiers) compared to +0 for the commoner.
The fighter has armor proficiencies which enable him to get a much better AC (say, AC 16 for chain mail, compared to AC 10).
The commoner deals 1d4 damage with an unarmed strike (or up to 1d6 with one-handed basic weapons, and up to 1d8 with two-handed basic weapons). The fighter can deal up to 1d8 with one-handed martial weapons or 1d12 with two-handed heavy weapons, and will likely be able to increase the damage further because of a positive Strength modifier.
By spending an action, a commoner may grant another commoner (or some other creature with Mob Tactics) a +1 bonus to attack rolls and damage rolls to a target while it is within his reach. The fighter gets Combat Superiority and a Fighting Style.
Still, I suppose we can be comforted that the human commoner has more than 1 hit point (four times as much!) and the human fighter does not have more than 30 hit points (less than half that!) and that the human fighter can't increase his damage by +1[W] once per encounter. All the other differences pale in comparison, really.