Answering the question you asked. Re-using the same passphrase for both of these purposes is reasonable, given that you control both the Linux server (where it's used as a login password) and the Windows client (where it is used to unlock the SSH private key), and assuming that you keep both machines relatively secure.
The purists will say that you should never reuse a password. In theory, this is fine advice. But it fails to take into account the tradeoffs, and it fails to account human nature. We're human; our ability to memorize complex, meaningless passwords is limited. It's one thing to memorize a single passphrase that is long and strong. It is harder to memorize two -- and impossible to memorize 100. If we took the advice to "never reuse a password" seriously, then we'd need to have dozens, possibly hundreds, of passwords -- and, given human nature, the consequence would be that each of those passwords would be inevitably be weaker. They might all be short, or predictable, or slight variations on the same phrase. And that is arguably a worse situation than picking a single very strong passphrase and re-using it in this scenario.
So, if you can find a way to memorize them two different passphrases without compromising on their strength, that's the safest course. If you can write them down somewhere where noone else will have access (maybe on a slip of paper in your wallet?), that's perfectly reasonable.
But if you find yourself unable to memorize two long and strong passphrases -- if you find yourself dumbing down the passphrases, so you can remember both of them -- it is not unreasonable, in my opinion, to use the same passphrase for both purposes. It does open up some risks. For instance, if someone breaks into your Linux server and cracks the password hashes, then breaks into your Windows client and steals an encrypted copy of your private key, they'll be able to decrypt it. Or, if they get a keylogger onto your Windows client and are able to record your SSH passphrase, they'll be able to break into your SSH server. However, those risks may be acceptable, in exchange for having a strong passphrase.
An even better answer. However, I think there's an even better answer that you may not have recognized yet. If you're using SSH to log into your Linux server, you don't need a password for your Linux server! You can add your SSH public key to your
~/.ssh/authorized_keys file, and then log in using public key authentication. At that point, you don't need a password for logging into the Linux server. Now you only have one passphrase you need to remember: the one to unlock your SSH passphrase.
Personally, I think this is the best answer of all. SSH public-key authentication is more secure than password-based authentication. So, this is my recommendation.
(OK, OK, you might need to have a password for your Linux server's root account and other accounts after all. But I suggest you choose a very long and random one, one that you will never attempt to memorize, and then write it down, seal it in an envelope, and store it somewhere safe. You'll never use that password. It exists only as a backup, in case you get locked out of the server. Since you never plan to use it in ordinary use, it doesn't need to be memorizable, it can be as long and strong as you like, and it can be totally different from all the passphrases you regularly use.)