Personally, I really like this topic. I like it because this question comes up very often, and it would be good to discuss it in one thread rather than in a dozen different ones.

I also want to note one thing: someone here noticed that a lot depends on the general (or something like that). This is certainly true, but it still wouldn't hurt to find out which units are stronger.

Now to the point: in a one-on-one fight, I am sure Archangels will defeat any other level 7 monster (the ones you can buy in the Castle).
To avoid speaking without evidence, I will provide a few calculations (if I made a mistake anywhere, I would be grateful if it were pointed out).

1) Archangel vs. Ancient Behemoth (probably the most frequent claim I've encountered is that the Ancient Behemoth beats the Archangel 1 on 1).

Assumptions:
1) No one gets a Luck proc during the fight (damage boost).
2) No one gets a Morale proc during the fight (extra turn or skipped turn).
Since the Archangel has +1 Morale, the second assumption favors the Ancient Behemoth in the calculation.

Damage the Archangel deals per hit: 50 (base) + 11 (difference between Archangel's attack and Ancient Behemoth's defense) * 2.5 (5% of the base 50hp damage per 1 point of attack superiority) = 77.5, rounding down gives 77.

Damage the Ancient Behemoth deals per hit: 50 (base, taking the maximum, although it could be less) + 13 (difference between Ancient Behemoth's attack and Archangel's defense, taking into account the Archangel's 80% defense reduction) * 2.5 (5% of the base 50hp damage per 1 point of attack superiority) = 82.5, rounding up (I rounded the Archangels down!!!) gives 83.

Turn 1: Archangel waits. Ancient Behemoth either moves to maximum distance (or not maximum, it doesn't matter). Archangel hits for 77hp, Ancient Behemoth responds for 83 (Status: Archangel 167 health, Ancient Behemoth 223).
Turn 2: Archangel hits for 77hp, Ancient Behemoth responds for 83 (Status: Archangel 84 health, Ancient Behemoth 146). Ancient Behemoth hits for 83 health, Archangel responds for 77 (Status: Archangel 1 health, Ancient Behemoth 69).
Turn 3: Archangel hits for 77 hp, killing the Ancient Behemoth.

As you can see, even in the best-case scenario for the Ancient Behemoth, the Archangel wins.

2) Archangel vs. Archdevil (I saw a claim that the Archdevil would win with its no-retaliation ability).

Assumptions are the same as in the first calculation.

Damage the Archangel deals per hit: 50 (base) + 2 (difference between Archangel's attack and Archdevil's defense) * 2.5 (5% of the base 50hp damage per 1 point of attack superiority), then multiply all this by 1.5 (hatred for Archdevils) and we get 82.5, rounding to 82.

Damage the Archdevil deals per hit: 40 (base, taking the maximum, although it could be less) - 4 (difference between Archdevil's attack and Archangel's defense) * 0.8 (2% of the base 40hp damage per 1 point of defense superiority), then multiply all this by 1.5 (hatred for Archangels) and we get 55.2, rounding to 56 (again, unlike the Archangel case, rounding up).

Turn 1: Archangel hits for 82hp, Archdevil responds for 56 (Status: Archangel 194 health, Archdevil 118).
Archdevil hits for 56hp (Status: Archangel 138 health, Archdevil 118).
Turn 2: Archangel hits for 82hp, Archdevil responds for 56 (Status: Archangel 82 health, Archdevil 36).
Archdevil hits for 56hp (Status: Archangel 26 health, Archdevil 36).
Turn 3: Archangel hits for 82hp, Archdevil dies.
As you can see, even in the best-case scenario for the Archdevil, the Archangel wins.

3) Archangel vs. Titan

Assumptions are the same as in the first calculation.

Damage the Archangel deals per hit: 50 (base) + 6 (difference between Archangel's attack and Titan's defense) * 2.5 (5% of the base 50hp damage per 1 point of attack superiority) = 65.

Damage the Titan deals per hit: 60 (base, taking the maximum, although it could be less) - 6 (difference between Titan's attack and Archangel's defense) * 1.2 (2% of the base 60hp damage per 1 point of defense superiority) = 52.8, rounding up!!! gives 53.

Turn 1: Archangel hits for 65hp, Titan (Status: Archangel 197 health, Titan 235).
Titan hits for 53hp, Archangel responds for 65 (Status: Archangel 144 health, Titan 170).
Turn 2: Archangel hits for 65hp, Titan (Status: Archangel 91 health, Titan 105).
Titan hits for 53hp, Archangel responds for 65 (Status: Archangel 38 health, Titan 40).
Turn 3: By dealing 65 damage, the Archangel wins.
And again, despite the Titan fighting with ideal damage, the Archangel won.

I see no point in calculating the fight with the Azure Dragon, because although its defense and attack are 1 higher than the Titans', its max damage is only 50.

Now on the reasons for victory:
Despite the Archangel having 250 health, it gets an extra hit (minimum 50 health) due to its speed. Also, its defense and attack stats are better than those of other units