They're cheap, they're quick to construct and it's handy to have these things on the shopping list when a new king takes over and you want to gain him the 'builder' V&V in as short a time as possible for as little cost as possible.

As well as beefing up your defences and making assault battles tougher for the AI, their description texts do say that they help reduce siege casualties to your side. It has to be said that AI castle assault battles are rare and the sit'n'wait routine is more common, so the second type of benefit is the most likely thing you'll see.

The castle build is 12 years, the citadel build is 20. It's up to you to decide whether or not it's better to do without the intermediate level of protection while you are waiting. I think you'll find that the next level of castle does incorporate these extra features anyway but, if I was in a position where the next castle level was more than my treasury can currently afford but I can afford the enhancements, then I will build them while I'm biding my time and saving up for the bigger purchase.

Obviously, if money was no object and 3-6 years of upgrading was an unacceptable delay in producing the types of troops the next castle will enable me to make, then I'll skip the upgrades and get building right away.

It also makes the difference whether the province borders onto another faction or not. If safely out of reach of enemies, I'd go straight for the next castle level and save time. At the border, it's a bot more touch and go. They only need to attack and siege you for a year and pull out to interrupt the build and you lose your money and have to start from scratch. In risky situations like this, I go for the cheap/quick upgrades and hope the extra defences are sufficiently off-putting to keep the enemy at bay while the more expensive builds are in progress.

Bit of a convoluted reply but I hope this helps.