I think the best reference is NIST SP 800-63 Appendix A, which lays out the theory and the calculations. NIST assumes that the dominant defensive strategy is entropy, and that passwords with maximum entropy are the strongest. Steve Gibson's password haystacks challenges that assumption and asserts that length is more important than complexity or entropy (in part due to the magic of hashing). For your purposes, I think that it is sufficient to assume that the strength of an authentication credential (password/passphrase/etc.) is derived from both length and entropy.
A sentence is stronger because it is longer. Granted, English text is highly redundant Approximately 1 bit of entropy/character, most attackers will fail to take advantage of that entropy. I have been out of pentesting for about five years now, but at the time when I last did any pentesting, attack tools assumed that the password was more similar to a word than a sentence. Password length to entropy is not a linear function for reasons that Henning Klevjer has explained fairly well, and the attack tools take advantage of those limitations. (IIRC, the issues that Klevjer raises can result in a 100fold increase in password cracking speed).
Based on those assumption, the sentence as a passphrase is particularly strong. As others have pointed out, researchers have attacked passphrases, but I'm not aware of any published information that real world attackers have done so.
However there is a significant limitation to the passphrase. The relying party (the site to which you're authenticating), must accept a passphrase. In my personal experience a significant fraction, possibly a majority of authentication sites will not accept a sentence as a passphrase. (I would appreciate anyone who can point me towards hard numbers on this) Many password implementations either explicitly reject passwords of more than 16 characters, or else truncate longer passphrases to the desired length.
Examining your use cases in turn:
1) home computer - Depends on your OS, but there are non-password authentication mechanisms which are far stronger and far simpler. (biometrics and hardware tokens e.g. Yubikey )
2) Internet accounts (email, online shops, social networks,...) - I doubt that you'll be able to use a sentence passphrase. Many if not most of these will not accept a passphrase - your only hope is to maximize the entropy of the password you supply and to avoid re-using the password
3) Internet Banking - As above, unlikely to accept a passphrase. However increasing number of websites accept two-factor authentication from RSA or Yubikey or soft keys like google authenticator.
4) Storing highly sensible data - I'm not sure what you mean here. If you are storing highly sensitive data, your best bet is offline, or encrypted. If you're talking about real encryption, then a sentence should be stronger, if the encryption product will accept it. Personally, I'd go for two factor authentication here and skip the password.
Also note that the strength of the password is meaningless if the relying party has a brain dead implementation - for examples see Sarah Palin Hack or Mat Honan. Your ultimate entropy cannot protect you against a negligent relying party. If you make the authentication credential strong enough, a targeted attacker will resort to an alternate method (of course you can cost him time and deter the opportunistic attacker). In such cases you must devote attention to both preventing the compromise and detecting/recovering from the compromise. But that's outside the scope of your question.
Please don't be distracted from the goal - if your real goal is strong authentication, then your best bet is to use a federated identity credential with a high level of assurance, and use a two factor authentication for that identity.