Public apps use HMAC-SHA1 for signing and three-legged OAuth 1.0a. The generated token expires after 30 minutes and then the user must re-authenticate to get a new access token.
Partner apps use RSA-SHA1 for signing and three-legged OAuth 1.0a. The generated token expires after 30 minute like Public apps, but with Partner apps the developer can renew the token when it expires without the user reauthenticating.
There's no real benefit to managing multiple connections though, it just makes your token management more complicated. It won't give you additional rate limits.