This is an interesting point -- and one with which I agree. IMO, this is where the uneven level advancement in AD&D was important, as well as the "unfun" roleplaying restrictions.
Sure, when you compare a starting 1e fighter and paladin, the paladin is immune to disease (not a huge deal at 1st level) and can cure diseases in others, can detect evil at will, has a +2 to saves, and can heal 2 hp/day. Those are nice, but not really a huge deal. In exchange, the paladin has to take 10% of all treasure off the top, then give away most of the rest, after expenses. The magic item restriction is probably not relevant at 1st level.
The paladin requires more XP to advance than the fighter, which means that, assuming even XP totals, the fighter will tend to be a level ahead of the paladin roughly half the time by 5th level. Additionally, because the paladin had to dump at least a 17 in charisma and has to have both a high strength and wisdom, the fighter is pretty likely to be gaining 10% more XP than the paladin, which can add up. This is also where the XP gained from treasure really helps the fighter, since the DMG says that treasure either needs to be made portable or stored in the PC's stronghold to grant XP, implying that only treasure kept is counted and the paladin has to give most of his away. Even if you only count the tithe against him, that's still another 10% additional XP that the fighter gains over the paladin. That puts our theoretic adventuring buddies about 200k XP apart by the time the paladin gets spells. At name level, the fighter will be gaining 3 levels for every 2 the paladin gains, without factoring in that 20% bonus. The ranger also has the high stat requirements, slower progression, and treasure restrictions, though not as pronounced.
Based on the above, the "balanced" solution for 5e fighters, who have the same advancement as their subclasses, would be to ensure the fighters always have a better BAB progression. Who would balk at giving the 3e fighter a 1.25 BAB progression? If 5e flattens BAB progression, maybe the 5e fighter just gets a flat +2 throughout his career. I'd also work bonus damage in there, but the fighter would be a bit more attractive, with just the BAB change.