Do you have any suggestions or examples of how to write a fight that shows two fighters are equally skilled?
This (basically) never happens in the real world. There isn’t one skill you use in combat, instead, it’s the culmination of a lot of different skills. So, you can have two characters who are equally matched, but two people of “equal skill,” are rare.
How you approach combat will be a result of a number of factors, including your skills, background, and the situation you find yourself in. This will almost never be identical between two combatants. Even if they share a background, and have the same goal in a fight, they’re likely to have slightly different skills, even if that’s been the result of focusing on different things in training.
Usually, what you’re looking for are fighters who are evenly matched. This isn’t a semantic distinction; one suggests that the characters have similar (or identical) skill sets, the other indicates that, after you factor things like their weapons, or situational advantages, it’s a toss up who will win.
So why am I saying this basically never happens? Because violence doesn’t work that way. If you know what you’re doing, you’re not going to be looking for an even match-up to fight, you’re going to be looking for an advantage that you can use to keep your opponent from seriously injuring or outright killing you. So, for two skilled fighters, it’s more likely to be about finding the right time to engage, so that their foe can’t respond, rather than, “a fight.”
It’s easy to confuse the concept of a ritualized duel and a fight. In the former, there are rules which must be adhered to, and the entire system is designed around the idea of fair and equitable combat. In an actual fight, you’re not being graded on your fairness, only your ability to survive the experience.
It is possible you have a character who has a singular skill set. This is a little too broad to inventory all the potential examples, but they’ll bring certain tricks and advantages with them into any fight. It’s possible that eventually they’ll go up against someone with the same background and skills. This isn’t really about being “of equal skill,” as dealing with a foe who knows how to respond to their normal advantages. Also, the more unusual their skillset is, the rarer this will be.
For example: A spy in conflict with another spy will be familiar territory. The intelligence community is small, but facing off against rogue agents, or hostile intelligence officers is part of the job. In contrast, a superhero dealing with someone who has access to the same power set, especially if they’re not used to dealing with powered opponents, could be extremely disorienting, given they may be the only two people to share that power set.
In these kinds of cases, the lead in is probably going to focus on realizing they’re dealing with someone who’s working from the same, or a similar approach to the one they’d take. In some unique circumstances, they may even be implicated simply because their normal approach would be instantly recognizable. (This is especially true in the superhero example above. Though, it’s possible one spy would try to frame the other. There are a lot of options here.)
Even in less spectacular situations, two duelists who trained under the same swordsmaster may have picked up a lot of similar quirks. At that point it’s not about having equal skill, so much as having a shared pool of skills. This can strip a lot of (relative) advantages that a character normally enjoys, because their foe can use them as well.
So, stepping back, you show this by how their opponents are different from their normal enemies. You show it by presenting an opponent who can keep up with them. Sometimes, who knows what they’re going to do next. You present a foe that your character needs a new approach to deal with. A foe who can use their own tricks and techniques against them.