Oxford or LSE

Depends on the course, also on how you define "harder". Some courses tend to be statistically more competitive at LSE than Oxford (or Cambridge) - offhand I think most years law at LSE has more applicants per place and thus a lower overall success rate, and economics I think is similar.
However there may be more self-selection out of applying to Oxford (or Cambridge) in the first instance which may skew the numbers anyway.
Ultimately a competitive applicant for Oxford or Cambridge is likely to be a competitive applicant for LSE and vice versa.

Thank you! I’m looking at PPE and I’m thinking of applying to both but I want to know which one is harder.

I doubt there is significant difference in competition between the two. If you're competitive for one you'll be competitive for both. If you're not competitive for one you probably aren't competitive for either. The main things to note regarding admissions are that LSE are very personal statement heavy as they do not interview, while Oxford have the interview and I believe the TSA. LSE also has slightly higher and more specific standard entry criteria of A*AA with A* in Maths (whereas Oxford requires AAA).
I'd focus on the course differences otherwise which are quite significant in that the LSE course is 4 years whereas the Oxford course is 3 years. The LSE course also has more scope to do more advanced mathematical and statistical methods courses and more mathematically sophisticated economics options I believe. There is also I believe some scope to take options outside of the three PPE areas during the LSE course. Also bear in mind at Oxford ordinarily as I understand it after first year students just focus on two out of the three areas, whereas in the LSE course all three pillars are mandatory throughout the degree.

Oh I’m so sorry, i meant just Politics and Economics. I know for that one I need AAA and one maths (which I’m doing) FM is deemed as least competitive as they want a broad of different subjects.

Ah that's rather different. You'll have to tailor the PS to LSE then but may want to try and allude to something philosophical for Oxford's sake...maybe something in the political philosophy/theory regime.
In that case obviously the big difference is you won't be doing philosophy in first year as a required subject and may not do any at all, at LSE. Whereas at Oxford obviously it's compulsory for first year at least.
Also note that politics and economics at LSE entails taking the less mathematical maths methods/economics options for the most part and you can't take the more mathematical options I believe, typically. This may or may not be a factor.

Yes I checked, that is fine since I don’t do FM rather just Maths; which is great for me since they prefer just having one of them than 2 for PE in LSE. I’m reading Yanis Varoufakis’ And The Weak Suffer What They Most?. Would this be a good book to write down?

It's not about whether it's on some hypothetical (and non-existent) list of "magic bullet" books that admissions staff look for. What they're actually looking for is what your critical analysis of the text and reflections upon it in the context of your proposed area of study are, and how well you communicate those and link them to your motivations for studying the subject.