You could look at them as two sides of the same perspective: Paul is saying basically that competition doesn't exist because if you focus on the customer need enough it ensures uniqueness, and Peter is saying don't copy what someone else has done, be unique.

Focusing on the customer enough does not ensure uniqueness. It is very possible to be in a market where customers needs are satisfied.

Zappos?

Zappos is not unique. They don't have a monopoly on anything and ultimately sold out to Amazon probably because there wasn't a way to grow much beyond their market of people who pay premiums on everything to get easier returns.

I think competition on a "macro" scale isn't what counts, it's more the competition at any given moment in the user's story.

When they hear about it or get the invitation, do they get it via a medium filled with a lot of spam?

When they follow the invitation, and see your service for the first time, will they go through the onboarding process?

After they complete onboarding, will they have a compelling reason to come back? Such as transactional notifications?

If they come back, will they form a habit in their mind of using your service for something? This is the "mindshare" that you are fighting for, that is the level on which competition really matters. How do you position yourself?

What network effects, social proof and social convenience / pressure will cause the person to use your service?

What are your customers currently paying for that you can do better / cheaper?

etc.

I think they are not necessarily mutually exclusive, just different ways to look at things. A good marketer can "invent" a new area of competition where you are the leader.

Thus, one aproach is to tackle this problem at the start, the other is to tackle this problem later on.