As far as I can tell, Mace Tyrell wasn’t a knight at all. So you’re comparing Mace who was never a knight, to Tywin who was in fact a knight. Lol
You can't tell, because no one is is going to address the
Lord of Highgarden as Ser. It would be considered a deliberate sign of disrespectful and contempt.
Primogeniture is the rule of the land whereby the firstborn son takes all. What greater honour is there left for the sons that follow beside the honour of being a knight? There are only 7 in the Kingsguard, and that used be exclusively for knights. You need brains to become a maester.
You can assume all lords in the south are knights, and that all nobles that can be aspire to be, especially so when they have no prospects of inheriting.
Add to that, below lords there are landed knights. Some by inheritance, but all begin with service. Like Davos, who was knighted by Stannis who is also never referred to as a Ser because that shit would not fly.
It is EXTREMELY likely Mace is in fact a knight. The books describe him as looking like he was strong once, so perhaps he is an oaf, but perhaps was also a capable fighter, though I doubt that.
Pride of place was given to Mace Tyrell, the Lord of Highgarden, a once-powerful man gone to fat, yet still handsome. His sons followed him in; Ser Loras and his older brother Ser Garlan the Gallant. The three dressed alike, in green velvet trimmed with sable.
As I say, knighthoods are cheap.
Tywin, coming from a big house as his was, got the best instructors money could buy. Later he became a knight, fought in a war alongside young Aerys and Robert's father and survived without any major injuries.
No stories will be told about his talent for sure, but he knew how to hold his own. Being mediocre with great armour/weapons is better than being great with trashy armour/weapons
Knowing how to swing a sword in the safe confines of courtyards under the watchful eyes of guards and instructors is one thing, and that's assuming Tywin knew how to swing well. It's another matter entirely to hack a man to death.
For all we know Tywin hung back and saw no meaningful close quarters combat or never participated in a melee at all. He was heir to Casterly Rock after all.
I also disagree on the last sentence. Unless they are so despite their utmost efforts, mediocre fighters are unlikely to know their own limits or that of their equipment. Fighting is a mindfuck, half the battle is keeping together between the ears.
Drogo and Daario can take a life without thinking twice about it. As easy as picking up a glass of water.