Some companies require similar training to be given across all branches, do you think this is correct or should each country's training be different?

Training modules shall vary from organization to another according to its business needs and culture

I think each  country should be different across the world because each country has its own culture and language which needs different training. Similar training requires only basis on the product.

If you are conducting training in same company and same country with different branches and the audience or your employee belongs to same cultural background or same work experience background. In this case I would go for same training.

But if your audience or employee comes from different background. I would suggest your to do training need assessment here. Highlight key improvement area or success factors (tailor made training) and make a master plan then deliver that to all branches. It will be healthy.

Final case. If same company with different counterparts training NO. It should be different because there is possibility that same technology, work environment, culture, rules and regulations, policy would be different then parent company. You will need detailed PEST, SWOT Analysis and need training need assessments too. I hope its helpful. 

Training should definitely differ from one branch to another let alone a whole country , customs  traditions , religion, politics and even weather are different in each country , whats wanted in Lebanon for example wont necessarily sell in KSA. 

Yes, training is needed on a daily basis, training given has to be with the same procedure and formats to make it more uniform and there will be stabilty.

I believe as a human we all have different learning styles which are acquired from lot of factors at the period of learning. Hence depending on their skills, culture, values and many other competencies change in course delivery might differ. However, key content shall not be affected or else the idea of training is defeated.

Depends on the course does it not. 

Standard Operating Procedure (SOP) is the best way for communicating in a business even though their is an issue about the culture but if we are following the SOP system of the company i think culture is not a big issue. So for me  it's correct to require similar training for all branches.

Staff development and training is an important aspect of job and non-compliance is often a crime in countries with strict laws, so,  what they should be? Answer is dependent on these local laws, also, skills and educational level of an employee has an equally important role to play in determining the extent of training to be given to employee. You cannot compare a professional with high school student could you?.

Example Is the field of Audit and Accounts the firm that has its offices in Pakistan / U.S.A. / U.K. shall need to work on the trainees at different level, because of the educational gap between these countries.

Training should be customized to suit the needs of the learners. This requirement will differ from each branch, city and country. While some basics like company policy can remain the same, the training objectives will not be achieved till it is customized to each audience's needs. 

Professional training should always be same but if it is other than professional training than its varies from country to country.