MAJOR, MAJOR EDIT to remove stupid statements on my part. My profound apologies to Marty Walser for them.
I have some objections to some of the analysis in this article. (of which possibly the most important is that we haven't actually seen what the final 5E monsters stats are yet - we're over six months out of date!)
Comparing Base Attack bonuses is problematic, as the additional bonuses are much more significant in 3E. It is quite possible for the actual attack bonus of a 20th level fighter in 3E to be very close to 40, although I'd say it's often closer to 35.
The attack bonus of a AD&D fighter at 20th level is actually quite difficult to evaluate, as it depends greatly on magic items (as there are no "expected" wealth tables). Perhaps +21 to +25?
D&D combat isn't just attack bonuses though - the actual relationship between attack bonuses and armour class changes between editions. In AD&D, higher-level monsters tend to still have ACs in the 2-9 range, which is, in a lot of ways, similar to 5E's bounded accuracy system. However, the attack bonuses (particularly of the fighters) have continued to increase, so high-level fighters hit quite often. Meanwhile, 3E increases ACs of high-level monsters significantly. Later monster manuals increase them even further. AD&D does have a few exceptions to this rule, generally powerful extra-planar creatures, but the actual implications of a negative armour class in AD&D are worthy of much more analysis than I have space for here.
Likewise, the relationship between damage dealt by weapons and hit points needs to be taken into consideration. AD&D, once again, has fairly static damage codes for the fighter. The girdles and gauntlets could boost that damage significantly, but there's no expectation that they'll be discovered. A fighter could quite well be doing no more than 1d8+5 damage with each of his two attacks at very high levels - but he'd be hitting most of the time. In contrast, 3E has some significant bonuses to damage - consider properties of flaming and frost, as well as weapon specialisation bonuses and the effects of Power Attack. The amount of damage a high-level fighter deals in 3E is significantly higher than in AD&D, and creates conversion problems there. 3E tends to devalue hit dice as a level of threat compared to AD&D, as well as adding in large constitution bonuses to hit points.
D&D Next (playtest version), in contrast has fighters attacking more often and dealing more damage than AD&D, but to nowhere the extent of 3E. It will be well worth doing a full evaluation in a month's time when the Basic Game is out.