UK Vs US Version

None, surprisingly - it may even be slightly longer: changes were made before it was certified, which is pretty common in the UK (it happened with the last Bond film, with that pre-cut version also be released in the US).

http://bbfc.co.uk/releases/grimsby-2016

The elephant scene may be slightly shorter in the US version, though that's not confirmed yet:

https://melonfarmers.wordpress.com/

It seems that according to a video interview with Sacha Baron Cohen that the film also suffered category cuts in the US to achieve an R rating. It seems that censors from the MPAA were convinced that an ‘elephant scene’ fell into the category of bestiality. (But surely bestiality would need to be cut at any level and wouldn’t be suitable at NC-17 either).

Cohen says that he challenged the MPAA’s definition of bestiality and also cut 6 minutes from a 9 minute scene. He suggested that the cuts were a ploy to obtain the scene he wanted and that the cut material had been added just to be offered as cuts in negotiations.

The UK was a 15 but it had the exact same content, British people must have bigger balls