If my fighter is going dungeon delving, just to pick a common example, I would be inclined to go with Breastplate (AC 14+Dex mod), both for the lightness and no disadvantage to stealth.
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if you were a Fighter in AD&D, you had your choice of armors -- study but light armors for dungeon and city adventures, heavy armor for when the crap was about to go down.
I can see this in principle but have never encountered it in practice.
At 1st level in Moldvay Basic, if my fighter can afford plate armour (60 gp from memory, so most likely) it is virtually suicide not to use it: dropping the hit chance from 6 in 20 to 3 in 20 (or thereabouts) is effectively doubling my life expectancy. At higher levels, where I have the hit points to open up a wider range of choices, I probably have magical plate mail, which (depending on which bit of DMG text you read - the rules as stated in the Armour section near the start are different from the rules stated in the Magic Item section near the end) either encumbers at one step lower (so comparably to studded leather) or not at all.
(I'm following your lead in somewhat mixing my editions. I can't remember what B/X says about the encumbrance of magic armour.)
I'm thinking of the Moldvay Basic example of combat, where the first thing the fighters (dwarf and elf) do is engage the enemy with ranged attacks.
For whatever reason, people said, "Forget all that," and tended to just specialize in one weapon
At low levels the fighter in my 4e game - who also is proficient, like the AD&D fighter, in longbows - would often open up with ranged attacks. At 28th level he is unlikely to hit with a longbow on much less than 20 (having not pumped DEX very much, and having only a +1 longbow to work with - but having not pumped solely CON either - off-STR stat bonuses have been allocated across DEX, CON and WIS), but from time-to-time he will make ranged attacks with his Mordenkrad that is enchanted as a heavy thrown weapon.
Specialisation has been mechanically driven - weapon specialisation in UA, retained in 2nd ed AD&D, was chosen as the mechanic to drive fighter attack rates and attack and damage bonuses. Skill-based games like RQ and RM similarly make choice of weapon a far greater determinant of combat ability than general martial expertise.
Magic weapons also factor into this - if I have a +4 two-handed sword and an ordinary spear, the +4 to hit and 1d10+4 damage completely crowd out the longer reach with 1d6 damage. (Even with STR bonuses that apply to both attacks, the spear is still crowded out.)
Another factor is that the mechanics of D&D combat do not generate much incentive to favour (say) reach over weight. In AD&D reach gives auto-initiative in some closing/charging situations, but that is a relatively small benefit if combat is going to last more than one round - which it probably will at mid-levels and above, especially if my spear only does 1d6 damage.
The fighter in my 4e game does swap between weapons - his polearm and mordenkraad - depending on whether he wants reach/control or sheer damage. This has been driven in no small part by Dwarven Weapon Expertise (or whatever the feat is called) which means that his specialisation bonus straddles both weapon types. Another relevant factor has been that our game has tended to emphasise GM rather than player control over magic item placement - I have followed wish lists embellished by my own imagination and inclination, and magic item crafting has been of very secondary importance. This meant that I was able to place magic items of both sorts, thereby eliminating the need for the player to agonise of whether or not to "waste" resources on powering up a second weapon.
I like all-around, multi-role characters.
Multi-role characters are fairly easy to build in 4e, though of course to some extent it depends where I draw the role boundaries (eg is defender/controller multi-role, or is a defender really just a melee controller?).
All-around is a different thing. The closest we have in my 4e game is the paladin, who can fight in melee, has a small complement of ranged spell (prayer) attacks, can heal, and has top-notch social skills. The sorcerer is also pretty versatile - good mobility and combat (including at-will short-range flight), good stealth, reasonable social but a little shaky once the damage starts raining down.
But I'm still not seeing how a fighter built using the 5e Basic PDF can deliver AoE attacks or do serious healing. Which is not a criticism of 5e - maybe fighters who can do AoE attacks are broken in that system? But I don't think 4e is as rigid, nor 5e as versatile, as at least some in this thread are claiming.
I'm not entirely sure where you fall. But presumably your 3rd level fighter with the DEX to take advantage of that breastplate isn't going to be as robust in melee as the 3rd level fighter whose player dumped DEX for STR and CON and is wearing the best heavy armour s/he can afford. That's a bit of role differentiation right there - in 4e terms we might be comparing a STR/DEX melee ranger to a PHB fighter. Admittedly your 5e PC can do something the 4e ranger can't, namely, put on a suit of plate, but you'll still be less effective as a bruiser than the character who was built to bruise from the start.
