Kraken vs. Coinbase in terms of safety

Hi y'all,

For several reasons, I'd like to change my exchange. I've narrowed down my choices to Kraken and Coinbase. I have the impression that Coinbase is a bit safer since it's a publicly traded company and a depository for giants like Blackrock and co. But what do you think? Is there really a big difference between Kraken and Coinbase in terms of safety?

Please don't respond with "no exchange is safe." I know, "not your keys, not your coins." But sometimes it's necessary to leave assets on an exchange to trade.

Thanks in advance for your answers.

I don't know if it matters, but I live in Europe.