I have taught mostly primary but did work in a secondary school for a couple of years a while ago now. What is your degree in? If you have maths, English, languages or science, you would be snapped up. If you love your subject, secondary enables you to teach your subject all day long. The older kids are more independent, you don't need to deliver them to their parents at the end of the day, go down to the dinner hall with them to get their dinner, help them put their coat on or tie their shoe laces etc. The flip side is that you might face a 6ft 2 angry, aggressive student at some points in your career or some bitchy girls too and / or they can be intimidating but again depends on the school and area. (That is not to say to say that this doesn't also happen with 9, 10, 11 year olds,l in primary it does!)
The secondary students can mark their own work in many subjects, and you can have "mature" conversations with some of them. Having worked in both, the workload is generally less in secondary, unless you teach secondary English or a few other subjects which require heavy marking. Teaching PE, Music, technology in a secondary school is quite light in terms of marking and if you love your subject, you get to teach it all day but I am sure there is also other workload demands.
If you would prefer to teach a variety of subjects from Maths to Art, Primary enables you to do this! The kids are needier, they want your attention, you really have to look after them as well as teach them and keep them safe etc as they are young. Ofcourse you have to keep the older kids safe too, but a 5 year old running around or leaving the building is more of a worry than if they are 15.
If you find it rewarding to give a sticker to a young child, see their smile, and give them lots of attention, primary might be for you but it is exhausting and their behaviour can be very poor, not as scary as a teenager perhaps, but they can destroy your lessons or prevent you from teaching. It's really hard work, with lots of marking of all the subjects you have taught in the day and you are expected to have good subject knowledge in every subject, whereas in secondary you teach the subject you know very well all day.
All of this though, is dependent on the school, how good or bad the Headteacher is, how deprived the area is, all sorts of things regardless of whether it's primary or secondary. The examples I have given aren't 100 per cent, as ofcourse an SEN 15 year old might need more looking after than a responsible 10 year old, but Inhabe just given examples on general.
Teaching is a very tough job primary or secondary. Your decision depends on whether you love your subject, the subject you studied, whether you'd prefer the kids to be more independent or whether you like the nurturing side of it. From my experience of primary, it's extremely tiring and the expectations have become impossible over recent years. I am sure secondary is the same.