The best light armor gives +2 AC, and if you take ability score increases into account all characters can easily manage the strength requirements for heavy armor.
Pardon, you're correct. I was confusing the late-end of the playtest (which had a type of light armor that gave AC 13+Dex) with the official release (which removed that).
So the Dex-based character's maximum AC is 1 less than a Strength-based character, if they're able to pick up Plate. However, at level 1, it is entirely possible to get the best light armor in the game (it's only 45g!). If you're Dex-based, your Dexterity can be expected to be about 16, for a bonus of +3, for a total AC of 15. This is better than the starting heavy armor (Ringmail, AC 14), but not as good as the next (Chainmail, AC 16). Since a Dexterity-based character gets two different kinds of damage improvement (melee and ranged) as well as defense improvement, there's little reason not to drop two ABIs into Dex, at which point said character has AC 17.
Strength-based characters can achieve
either the highest defenses (by 1 point), or the highest damage dice (1d10, 1d12, or 2d6), but not both (light armor+shield with +5 dex mod = AC 19, one point ahead of plate+2h weapon). Dexterity provides the midpoint: almost the best defenses (and better than someone wielding a 2h weapon), same max one-handed damage (1d8), and the ability to use bows which are the superior ranged damage option for both range numbers and damage dice (thrown weapons are d4s or d6s; longbows and light crossbows are 1d8). And, again, Dexterity gives a better or at least more common save, Initiative (which can't be improved any other way, AFAIK), and a much wider variety of skill benefits, which heavy armors impose Disadvantage on.
So, again, I still feel like there are
plenty of incentives for playing a Dex-based character. Particularly since fighting styles and (AFAIK) most maneuvers and spells do not specify a particular attack stat, so for Fighter (and Paladin, interestingly enough) most class features don't care which path you take. Attacking earlier, having second-best defenses, no loss of damage (if only using one-handed weapons), better ranged options, having bonuses rather than penalties to stealth and acrobatics, and improving a common save (at least in the early game) sounds like it is
well worth the trade-off of losing 2-3 points of average damage (1d8=4.5, 1d12=6.5, 2d6=7.5) ~or~ +1 AC, improved carrying capacity, a rare (but potentially dangerous) save, and athletic skills.
Doing much more than the above will, I feel, make the Dex-based Fighter--and in particular the archery-based Fighter--straight-up superior to the Str-based fighter most of the time. Whether you make the Str-based Fighter worse or the Dex-based Fighter better, any more relative improvement risks making Str not worth it to anyone who doesn't optimize heavily. Most "old-school" advocates I've known are rather heavily anti-optimization, and it seems that you feel the same way, so I wouldn't recommend changing things either way.