Yukihiro Takahashi's Beatles covers improved over the years. First his 1980s band The Yellow Magic Orchestra did a cover of Day Tripper that really didn't work, IMHO. I't on youtube but I wouldn't recommend checking it out. In the early 80s he covered "It's All Too Much" on a solo album, but it's OK and interesting, but not the best. His late 80s cover of Tomorrow Never Knows was good, but that's a hard song to do wrong and many, including The Beatles, have done it better. Same for We Can Work It Out His best covers in my opinion are Taxman as posted, and his version of "I Need You" on his 90s album "A Ray of Hope". It's again an electronic version, but soft electronic pop. IMHO he did a much better job at transposing the song into the electronic dance pop style than Candyflip did with Strawberry Fields Forever. Unfortunately his version of I Need You is not on youtube. Takahashi includes one cover track on each of his albums, of which he has released a LOT, and they are often Beatles songs.
Mentioning TNK reminds me of the version by 801. I love the bass playing on their version and would like to be able to play like that myself. I've never heard anyone match The Beatles version of it, particularly with the context of that being done in 1966! But, there are aspects of this I really enjoy, including the novelty of it being Brian Eno who is singing it.
Also, here's Japanese singer Mayumi Chiwaki turning A Hard Day's Night into a novelty number. Certainly not preferred to The Beatles, but I think the world is a better place for having this all vocal (sampling) version.