They're very different things, so it's hard to bring them under one hood.
PDF protection/encryption is a kind of joke, really. All in all, it's not made to withstand actual attacks. So the "benefit" is mainly to prevent your 8-year-old (or your 80-year-old parent) from reading a document. PDF protection is much like hiding caller ID when making a phone call. The device is asked to kindly comply with your request to deny the user certain functionality. A software that simply doesn't care will reveal the document.
PDF encryption, on the other hand, is actual encryption (making the text unreadable and unrecoverable). Except... unluckily, they're only using 40 bits from your password hash (at least, that was the case last time I looked), and 40 bits is, err... well... not really awesome. That's not just something you could brute-force in theory, it's something you can brute-force (without even resorting to the help of a dictionary) in a very reasonable amount of time with no-special stuff. As in, 2-3 hours on a modern desktop PC running single-threadedly. Or, well, a couple of minutes full throttle, for that matter.
On the other hand, ZIP/7z encryption is actually quite good. While still derived from a password, it uses a 256 bit key and AES encryption. Sure enough, few passwords, if any, have that much entropy, so... the 256 bits should be seen as "up to..." figure. But in general, as far as the implementation's limitations go, it's pretty good. The rest, that's your responsibility.
Now, what is the advantage when transmitting data over an insecure channel like TLS? Wait, did I say insecure? Indeed, I did.
TLS is secure only under the assumption that you can trust your certificate chain. Which, unluckily, is as far from the truth as it could possibly be. Not only do many antivirus tools on the end-user's computer install custom root certificates and intercept/decode TLS (and, at its own discretion, forward data to some hopefully trustworthy third party in e.g. Tomsk). Not only do CAs get compromised. Not only do several governmental agencies subvert the certificate chain, deliberately and systematically, only to decrypt your traffic. There exist companies (which are also Root CAs) that have packaged the whole eavesdropping thing into ready-to-use-no-tech-skill-necessary boxes, and are selling these to whoever is paying for it.
Sure enough, if you do not want (or cannot afford) someone on the internet to read your precious documents, then file-level encryption does add a benefit because now, all of a sudden, eavesdropping is no longer automatic, online-realtime, and trivial. Well, the actual eavesdropping still is... it's just that what you get isn't very meaningful. Assuming a good password and barring a wrench attack, it's very hard to get to the data.
Encrypted archives (not all, not necessarily, but usually) also have the benefit of hiding metadata such as the filename or size, i.e. you can't even tell what may be the topic, or whether it's worth an attack.
If you send an encrypted file named
plan_to_kill_president.doc, you can be sure to get monitored closely (or questioned) soon, regardless of whether the contents can be deciphered or not. If you send a document
patent_application_fusion_battery.doc, it's obvious to an eavesdropper that an attack on the encryption may be worth the effort. If you send a file
stuff.7z, nobody can tell. It could be anything and everything, or nothing. Fun fact: two identical archives encrypted with the same password are not even identical (that can come as quite a bit of a surprise to unsuspecting users!).
What about full disk encryption? Well, that sure is a kind of a hurdle for a laptop thief or a drive thief, but otherwise... the sad truth is that if you can read it during normal operation, someone else probably can, too. Getting to the data while you are logged in is, compared to breaking encryption, pretty easy, almost trivial.
An encrypted file on an encrypted volume is still encrypted, if I can access it. Sure, there are means of getting the password, but it's an extra hurdle that isn't all trivial.