I could have sworn in 1e AD&D 12 HP is POSSIBLE, but not necessarily a given (DM dependent of course). That would be a 1 in 10 chance of rolling that, with an equal chance of having only 3 HP. The average I think would be 7.5 HP so somewhere in the range of 7 or 8 HP for the Fighter.
How do you get 1d10+2/+4 damage from a longsword in AD&D? I'd think you could get 1d8 (+STR) or 1d12 (+STR). With 16 STR that should be a 1d8+1 damage or a 1d12+1 damage from what I normally play. If I were single classed and UA was available I'd specialize in longsword thus giving me a +2+1 (total +3)Damage there on that note, and eventually double specialize for a +3 damage making it 1d8+4 or 1d12+4 damage.
In 5e for damage I think if I were using a longsword with one hand (instead of 2 hands) I'd probably have a shield and go dueling which would give me another +2 damage. That would give me a total of +5 damage with 16 STR in 5e. Eventually I'd put more points into STR to get a 20 STR which would give me a +7 damage to my hits as in 5e you get to increase your Ability scores every so often as part of the game involved with leveling (just like double specialization is eventually something you could do as you level with AD&D with UA).
Uh, I was mis-remembering what a 16 Strength gave in AD&D, where it's only +1 damage. And yeah, I forgot it wasn't until later that max hit points at level 1 became standard, though it was a rule adopted by pretty much everyone I ever played with.
The 1d10 damage is for a two-handed sword, a weapon that I don't think I ever saw anyone use because dual wielding was so busted.
ECMO3 rightly points out that while the damage isn't hugely different, the chance to hit is. A 1st level Fighter hits AC 0 on a 20, same as all other first level characters. A 17 Strength is required to even get a +1 to hit. Weapon Specialization isn't core (not until 2e), but if allowed, it would give the Fighter +1 to hit and +2 to damage, along with 3/2 attacks per turn.
If you play an Elf, you get a +1 to hit with a long sword. Now if you luck out and get high 18 % Strength, you can have greater damage and combat bonuses than any starting 5e Fighter, but that's far from standard.
2e would add a few other modifiers, like Fine and Exception-quality weapons, Bladesong, etc. etc., but 1e also had improved weapon specialization.
The proficiency bonus alone gives the 5e Fighter a +2 to hit that the AD&D Fighter wouldn't have though. The numbers do change a bit when fighting large sized foes, but that's not something a 1st level AD&D Fighter should be doing.
If you'll excuse my shoddy mistakes in the previous post, my point isn't completely off-based. Monsters are tougher and deal more damage than they ever did in AD&D. Players aren't a whole lot tougher, though they do gain a few tricks they didn't have before, like Fighters having Second Wind, spellcasters having cantrips and more spell slots at low levels (but less at high levels). The players do hit more often, and they generally have better AC (though by 2e, it was possible to have a starting Fighter with AC 0, the equivalent of AC 20 without any magic).
My main issue with healing magic is it's effectiveness. In AD&D, you needed healing spells; natural healing would take forever to get the party back into the dungeon. One encounter could tap your Cleric out for the day.
Now it's true that 5e gives you more options to heal without magic, but when you compare the effect of healing someone as opposed to just using those same resources to kill enemies, it's pretty sad (and as D&D Reborn points out, the damage spells do isn't exactly stellar either, compared to the toughness of enemies in 5e).
Now sure, that Bugbear isn't hitting every turn for 2d8+2; his attack bonus is +4, and most 1st level Fighters have an AC of 16-18. OTOH, the AD&D Bugbear has the same chance to hit due to his 3+1 Hit Dice, and an AD&D Fighter could be rocking AC 3 with Banded Mail and a Shield, so that's roughly about the same.
Whether the Fighter has 1 hit point or 15 vs. what you could have in 5e is subject to a great many variables, but even if we assume the average AD&D Fighter has 5.5 hit points, and the average 5e Fighter has at least 10, we still have the issue that the 1e Bugbear does 2d4 damage and has 14 hit points on average, and his 5e counterpart does 2d8+2 and has
27 hit points, yet player side damage and healing hasn't improved to the same degree.