My utterly inexpert opinion (having seen the Branagh version exactly once) agrees with yours.

I know they did cut quite bit out. In particular, I was disappointed that they got rid of much of the "joke" Henry plays on Williams, although I suppose that's back to making Henry seem more sympathetic than perhaps he is.

But I think that this version is more faithful/leaves more in than the Olivier version did.

An open question: is there an obscurer but better film of Henry V?