From what I'm aware of both schools are high quality for your subjects but I'll give you my personal experience. I was accepted into LAET, attended for about 2 weeks, then dropped out and moved to a different school. LAET is stricter, has uniform, less freedom in timetabling and Woodhouse is the opposite. LAET might sound bad from what I'm saying but LAET will hence be more disciplined than Woodhouse in helping you achieve top grades whereas Woodhouse gives you the independence to excel. Both are high achieving schools that give students excellent opportunities through their connections and partners. Both schools are also eligible for contextual offers. The main difference is Woodhouse is more independent, LAET is more disciplined. So whilst one student may excel in Woodhouse, they may do terribly at LAET and the opposite can be true too. One thing I don't know is how good either pastoral system is but I there is a department students can speak to. Clubs and societies are relatively similar between both schools but LAET likely has more as being part of a club is a requirement at LAET. Woodhouse has one form group session a week bur LAET has one every day (I believe?). Also almost all schools have at least on bad teacher even the good schools, so take it upon yourself to get high grades.
About travel, depending on how you use your time travel can be an inconvenience or a real boost to your grades. At my current school I take two trains so I spend a lot of my time waiting and doing not much but listening to music or being loosely engaged with revision. If I was on a direct bus to Woodhouse, I could have my own space to revise very effectively even though it'd be a total 2 hours journey. At my current school I travel for about 1hour 40 a day.
Also you may want to get Uplearn as they offer all of your subjects on there. It's a revision site where content is taught. If you have circumstances (like you're a free school meals student) they'll give you access to all your subjects for free.
For reference I currently study chemistry, biology, maths and psychology at an independent school on a scholarship basis. I'll be transferring to Woodhouse for Y13 and dropping chemistry as I can't keep paying for travel and loads of other reasons.
Anyway I'll stop rambling now. Lmk if you have any questions and I seriously hope the best for you. Make the most of sixth form!