If you are the only one with access to the secret key, then you control the coins. If someone else has the secret key (or keys), then they control the coins.
I believe copay is okay from a brief glance, but I honestly can't tell if they give the keys to Bitpay for backup or not.
The safest wallet is bitcoin-core, though there are plenty of reasonably safe options.
I used bitcoin-core before, but I wanted to switch to a more light-weight wallet, and one which is based on BIP32. At that time copay looked like the best option. And because it's BIP32, I should be able to transfer the wallet to another compatible implementation without any problems.
I believe copay is okay from a brief glance, but I honestly can't tell if they give the keys to Bitpay for backup or not.
The safest wallet is bitcoin-core, though there are plenty of reasonably safe options.