...about something on the BBC?
Your complaint must be logged and investigated under the terms of the BBC's charter. You can complain about a programme even if it doesn't directly affect you, and even if you didn't see it at the time. If it is decided that any guidelines may have been breached there will be a further investigation. Action may be taken against those responsible for the programme/story in question. You can also complain to Ofcom, who have the power of unlimited fines. All this will be backed up by a torrent of media hysteria involving other newspapers and broadcasters, all of whom have a vested financial interest in seeing the BBC's credibility damaged and their own profits boosted, given that their primary responsibility is to shareholders, not to their readers.
...about something published by the Daily Mail?
Your complaint will be recorded and you might get a letter or email back. If it's about a story that doesn't directly involve you, you cannot take the matter further. If it does directly involve you, you can write to the PCC. The Mail can write a letter explaining editorial policy to you. If you aren't satisfied with that very generous offer, the Mail can write an apology if they deem it necessary. If they don't, or even if they do and you still want to take it further, and if the PCC - which is chaired by the editor of the Mail - decides the Mail has got it wrong, it could write a ruling that says the newspaper has got it wrong. There is no further sanction or redress, unless the Mail has libelled you, and even then, it's up to you to prove it has damaged you personally. You can get the case taken on as a conditional fee arrangement, but that's harder than it sounds, as the big players are only interested in upset celebrities, where there are opportunities for big payouts without the necessity of having to go to court, rather than ordinary people, where it can be argued that the financial damage suffered to their reputation was much less.
So, it's easy to see why the Mail has taken the moral high ground.