Hey Romi,
This is a little tighter than the other one, but I agree with Rami still.
Maybe I can be more specific this time though.
Throughout the verse you sing a straight rhythm whereas the original has a bit of a dotted rhythm going on.
It's hard to describe but picture the ride cymbal in a simple swing beat. The original has that kind of groove.
Of course your way isn't wrong: It could just be preference.
Loads of people change the rhythms a little to suit themselves.
When you kick into the next section, the chord strikes should fall just after the bold words.
I get
BY with a little
HELP from my
FRIENDS
whereas you're singing
I
GET by with
LITTLE help from
MY friends.
Again, do it whatever way you want.

Just pointing out the differences in case it helps.
Put simple, people could sing along with the verse, but not with the chorus. See what I mean?
EDIT: Weren't you right handed in the other video!