I don't think the Idiran lack of Mind level AIs and them losing are co-incidental.

The Gzilt did have their own approach, using virtualised and hyper-accelerated crew. We're not told much more about that and how it works, so it's hard to say, but it can't be anywhere near as efficient and capable as using Minds.

Spoiler for Surface Detail:

There is that battle where a single Culture ship absolutely destroys a GFCF fleet without breaking a sweat. The ship's Mind says they stood no chance because their AI didn't have autonomous authority over weapons systems and relied on accelerated crews for decisions.

What I love most is how the battle is explained to a human passenger over the course of several pages and at one point they have an exchange like:

   Mind: Now here comes my favorite bit.
   Human: What do you mean? This isn't live?
   Mind: Oh, no, the battle was over in fraction of a second. I'm showing you a slowmo replay.