It depends. Considering you can protect the private key with a password, if you use a strong enough password and protect the private key, then using the same key with all machines can work just fine. On the other hand, I usually use a number of unique keys for systems in the same risk category. For example, I use a key for a production server that I store on an encrypted USB drive. I use a different key for dev and test machines. Further, I don't use ssh keys to grant root access but rather access to my account.
The security implications for first method is that if the key is compromised (i.e. adversary gain access to both the key and password), then the adversary could have remote access to all systems. Since privilege escalation is much easier with any sort of system access, there's greater risk with option 1 than with option 2. However, option 2 only offers better security/lower risk if you protect the password and private key.