RSA PSS security advantage
Even if we make RSASSA-PSS deterministic by fixing its seed, it remains with a security proof in the Random Oracle Model per Full Domain Hashing (Jean-Sébastien Coron, On the Exact Security of Full Domain Hashing, in proceedings of Crypto 2000). We can't say the same for RSASSA-PKCS1-v1_5, because a lot of the message representative is fixed.

In practice, a better argument to use deterministic RSASSA-PSS rather than RSASSA-PKCS1-v1_5 is that vulnerable implementations of verification of RSASSA-PKCS1-v1_5 abound, when I know no vulnerable implementation of RSASSA-PSS verification (regardless of randomization), and this is less likely to happen accidentally.

However a practical argument against RSASSA-PSS is that it requires careful specification of the hash and the mask generation function: even if the later is almost universally MGF1, that could be with another hash (e.g. stuck to SHA-1) depending on implementations.