I'm sure while most ladies have favorites and preferences, but will see just about any client who isn't dangerous or looking to rip them off.

For someone that wants a regular situation, I can certainly see this being a factor. One is less likely to return if she isn't easy to deal with, though depending on level of difficulty it's not necessarily a deal breaker.

 
But for those who hobby and don't repeat much, it only matters in how it shows or impacts reviews. If other reviews point it out and lower scores because of it, it can deter business. Also, if as a reviewer this stands out, it can negatively impact the review given.  

 
But in the end, if she's good in the sack, dudes will often give a pass on the initial challenges and not even mention it. Because the brain in our penis has the final say.

Not that it’s required but I 110% approve of this dialog/thought experiment/compelling outlook…
Is this attitude being explored as an archetype for clients, providers, or both?
I’m enchanted

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You tell us. Do you try to outdo other agencies in your region?

Seems like some of the items mentioned could be seen on both sides, provider and client, while others are perhaps more unique to one side or the others. It's a bit odd to think of competition between client and provider, as opposed to supply side or demand side.

 
But I do think I get get some of what you're aiming and. I actually think it gets discussed a fair amount, though is not seen as competition but rather a clash of view point. Client that tend to view the interaction as more then merely a transactional sexual encounter where the physical sex is the whole point and anything else is either fluff or unwanted distraction often take exception to other clients that base their reviews on a broader metric and claim things like "shills", "lackeys for the girl/agency". Same does go in reverse where some see other reviewers giving out unjustifiably low scores. That's one example of where I see the "silent competition" playing out. It might be seen as competition to influence scoring standards by either side but generally just looks like conflict and argument to me.

 
Another area might be those client looking to be seen as better clients so perhaps getting more preferential treatment. That is pretty common in all lines of business. Some clients may both be willing to spend more -- more frequent appointments, tipping the provider or both -- and then expect various benefits (preferred bookings, advance notice of a favorite girl coming, or even early access (before any official start date). This can create conflict and concern with other clients if they think they are getting bumped or blocked in some way. While it's not been something that has been discussed recently, it's been a frequent and well discussed issue in the past.

 
So not entirely sure I agree with the framing that it is competition as one normally thinks of competition or that it's been some silent event no one has been talking about. But maybe you're thinking of something other than what I'm mentioning.