Question: Why are SHA3 algorithms considered more secure than their SHA2 counterparts? Surely in part, it is due to their resistance to length extension attacks. But specifically, when considering collision resistance they have the same O(n) attack times.

Is it because they are more resistant to preimage attacks?

Answer: 
TL;DR: the assertion "SHA3 is more secure than SHA2" is unproven when we consider collision resistance, or preimage resistance.

Addition: there are reasons to prefer SHA3, including being a more general tool since it's a plausible instantiation of a random oracle (contrary to SHA2 due to the length extension property). I refer to [this answer](https://crypto.stackexchange.com/a/95265/555) for more.

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We don't know which of SHA2 or SHA3 is more collision-resistant. Both try to achieve the best possible collision resistance for a $n$-bit hash, e.g. cost of $2^{n/2}$ hashes (within a factor not too far from 1) to achieve collision with probability ≈39% of success.

We don't know which of SHA2 or SHA3 is more preimage-resistant. Both try to achieve the best possible preimage resistance for a $n$-bit hash, e.g. cost of $2^n$ hashes (within a factor not too far from 1) to achieve preimage with probability ≈63% of success. That was not always the case: briefly, the preimage resistance of draft SHA3 was lowered, in the interest of making it faster, way below that (conjectured) for SHA2. But that change caused controversy and was reversed, see [this](https://en.wikipedia.org/wiki/SHA-3#Weakening_controversy). Now we have to use SHAKE when we don't want the arguably overkill preimage-resistance of SHA2, and prefer more speed instead.

Argument that we don't know: if we knew which or SHA2 or SHA3 is the most secure from the standpoint of collision or preimage resistance (by a factor larger than the speed difference, which makes the faster algorithm correspondingly less secure), one of SHA2 or SHA3 would be broken from that standpoint.
I know you already mentioned length extension attacks in your question, but I don't think the importance of that can be overstated in how SHA3 is *practically* more secure than SHA2 - especially whenever you'll be designing your own cryptographic protocols/systems on top of it. Thanks to length extension attacks, use of SHA2 may require active measures (e.g. HMAC) beyond the hash itself in order to use it safely, and *most people using it don't understand this*. Even if they do, the need occupies space in one's mental model that could be spent on more valuable things.

In addition, implementations of SHA2 may be subject to side channels that, in certain contexts, leak information about the data being hashed. This can be critical when the hash is used with key material, such as in HMAC or signatures. [This paper](https://eprint.iacr.org/2017/985.pdf) claims to successfully recover private keys from the (2017) WolfSSL implementation of Ed25519 using such a side channel. SHA3 by design does not invite side channel leaks.