that way your OTPs are less secure

Aegis backups are encrypted. One could argue that storing OTP seeds in someone else's server is even less secure, which is what Authy does.

because of security

Yeah, I read that too when choosing OTP managers and I'm not convinced. These security reasons they give to practice vendor lock-in just sound very convenient to them. They could very well add a secure bidirectional data import/export functionality like Aegis does. If they are really concerned about account takeover, they can confirm user identity, add delays with notifications before exporting, or add any similar bureaucracy. But if password managers allow exporting entire vaults, an MFA app can allow the same for OTPs.

And I insist on this feature because manually resetting over 40+ MFA codes that I have because there is no export feature is a REAL PITA.

Aegis lets you choose if you want your keys exported/backed up/included in the android backup. You have to setup a password to encrypt the storage and it came with every backup option disabled when I installed it. So should be safe.

Authy also has the option to backup to cloud. So you probably need to use Google Authenticator if you want to be locked out of your accounts in case you lose your phone.

I'd guess that it doesn't make a huge difference in terms of security.

Surely both apps encrypt the seeds they store, and surely you can't export seeds from Aegis before decrypting them (pin, password or biometric). If someone has your credentials (or encryption keys) to both these apps, and especially if they have physical access to your phone too, there will be ways of accessing the seeds whether there's an export function in the app or not.