Unless they've changed the system recently, the Ox MSt administrators wait until the final deadline in early January before looking at the applications, so it doesn't matter when you apply.
I read through some of the_alba's posts. Like I said, I didn't do the 1900-present day MSt, so I was interested to see her experiences. As far as competitiveness goes - that probably depends a lot on the character of the group you find yourself in. Getting in is especially hard for the modern period as I gather that about half of MSt applications are in that area.
A few things to bear in mind about the Ox MSt:
1. It's short - 9 months, over by the end of May. Good for having a summer off and obviously cheaper than having to sustain yourself studying for another 3 months.
2. It's intensive, especially in the second term where you currently have two assessed essays to complete in the final four weeks.
3. There are no exams - it's assessed by four extended essays and a couple of other hoops to jump through, like a 30 min palaeography test (which everyone passes).
4. Most people take two taught classes and write a paper on each of those, plus one bibliography paper and one dissertation. Options for the taught classes are quite limited - you may well only have two or three courses to choose from. For the other two papers you can write on pretty much anything you like - but, if you want to do a DPhil, there is a lot of pressure to make them both related to your eventual proposal. This can make the course feel quite narrow and specialised around your particular interests, which could be an advantage if you are sure about what you want to do a PhD on.
5. I don't know about how difficult it is to come into the Oxford DPhil without having done a MSt, but most people who do the MSt and want to do a DPhil are allowed to stay on - you don't need a brilliant mark in every essay. Oxford is also a idiosyncratic place and, if you do want to do a DPhil here, it does help to have had an extra year to build up contacts among the tutors (and very importantly, to identify a supervisor), understand the Bodleian, and work out the bureaucracy.
6. It's a huge English faculty, which means there are a lot of research / skills seminars and there are guaranteed to be potential supervisors and research students with similar interests to yours. Unfortunately that makes it less intimate than a smaller faculty. Supervisors have heavy undergraduate teaching and administrative workloads, so you often have to book appointments with them some time in advance. Having most of what you need in the Bodleian is a big luxury, especially for people studying earlier periods.
7. There are a number of compulsory, non-assessed MSt courses, a couple of which are not particularly well structured and can be tedious. The tutors responsible for each course vary a lot from year to year, so it is luck of the draw. There's a lot of focus on more 'dry' research skills that may come in useful later. The most popular optional classes may be oversubscribed and there is a small chance that you might not get on to one. There are a number of administrative irritations which I gather they are trying to address - the most annoying one saw my feedback for my dissertation never released to me so all I got was the mark. Essay titles had to be submitted a long time in advance and couldn't even be tweaked, which was frustrating.
8. I don't know how this compares to other Master's courses, but there is not a great deal of personal contact or feedback and you are expected to be quite self-reliant. You will be allocated a college advisor who may take a great deal of interest in your progress, or may just see you for five mins a term. You are expected to have an idea of what you want to study for the bibliography/dissertation essays from quite early on in the course, which is disconcerting if you were hoping to broaden your mind during a Master's course rather than specialise.
9. Oxford Uni computing services deserve a special mention for being highly efficient and useful.
Overall, I thought that my academic writing improved substantially during the course. The bibliographical knowledge and research skills are a good preparation for research. I also found the course stressful, the workload high, and wasn't able to read as widely as I'd hoped. It could be argued that the specialisation is a necessary evil; if you plan to continue to a DPhil/PhD, then you are more or less guaranteed to finish the nine months with a feasible proposal and a large amount of research and writing already completed on it.