I've looked at the answers for the question "How did cadet branches start?", and based off the information in that forum, I would like to know what rank equivalent to peerage the cadet branch could hold. Could they be given the ranks, powers, and titles equivalent to that of a duke or earl, or did cadets have something separate?
In England, as I understand it, a cadet branch of a house is simply descendants of sons after the first. They can be, and sometimes were, given peerages themselves. Let's take a look at one notable cadet branch.
If we start with Edward III Plantagenet, the King of England from 25th January 1327 until his death in 1377 there is a very good example of a Cadet Branch. Edward III had as a first born son, Edward, the Black Prince. He would have been King of England, had he not died a year before his father. Upon Edward III's death, his grandson, Richard II became King. Let's leave that line for now.
Edward III had lots of children. His third surviving son, John of Gaunt (so named because he was born in Ghent, Flanders, but that's another story) married Blanche of Lancaster, creating the (2nd) House of Lancaster (a Cadet Branch of the Plantagenet line). Their son Henry usurped the throne on one side of the War of the Roses. John of Gaunt, 1st Duke of Lancaster ended up providing Henry IV, Henry V and Henry VI, Kings of England.
In answer of your question, Edward the III's third surviving son was John of Gaunt, 1st Duke of Lancaster, with the title, lands and moneys they had. That is just one example of a Cadet Branch.
Peerage was not a guaranteed right to those later sons, however, but something that had to be gained by marriage, or granted. John gained his peerage by marriage to the heiress of the House of Lancaster. Without the marriage, he was just John of Gaunt, a son of the King.