The former. People flip out if you take away their
anything. See: the last 20 years of game design.
A kludgy fix to this kludgy problem could be to make some over-the-top feats that can only be taken by specific races. With, say, half a dozen "feat-and-a-half" feats, it'd be hard to argue that a Dragonborn is
bad, they just have to grow into their power.
Actually, that'd be pretty cool: make six feats, one for each ability score. You get +1 to that score, and a strong and thematically appropriate benefit associated with that ability score. Spitballing concepts rather than hard rules, using Dragonborn as an example:
- Dragonborn Fury: +1 Str, attack bonus when below half health, use breath weapon on a melee weapon for temp. [element] damage bonus.
- Dragonborn Toughness: +1 Con, reroll 1s on Hit Die rolls to regain HP, choose a second breath element, expend breath weapon to turn one of your resistances into immunity for a while.
- Dragonborn Guile: +1 Dex, proficiency in one of [dex skill list] (Expertise if you already have prof), expend breath weapon to create a concealing cloud for PB rounds,
- Dragonborn Memory: +1 Int, proficiency in one of [int skill list], reroll knowledge checks [PB] times per long rest (only one reroll per check),
- Dragonborn Senses: +1 Wisdom, prof in Perception (Expertise if you already have prof), Darkvision, advantage on checks to detect hidden treasure.
- Dragonborn Presence: +1 Cha, prof in one of [cha skill list]; expend breath to gain a supernatural aura of fear/awe (your choice) against all non-dragonborn humanoids, giving you advantage on all Charisma ability checks against them and imposing disadvantage on anyone trying to discern your true motives, alignment, etc. or oppose your threats/persuasion.
All "expend breath to X" benefits would last for something like Proficiency Bonus rounds or something like that. A small but meaningful amount of time--growing to be
about a whole combat by mid levels.