If you mean the process — they can differ in the details but not in the overall process. You'll always need to do cases and some personal fit interview, but they can differ for example in the number of interviews or whether they add an upfront online test or not.
If you mean the quality of profiles they are hiring — officially they do not differ. They look for the same profile, toolset and qualities - the job is very similar across countries. However, there can be differences due to:
Country-specific requirements — the main ones being language and visa, but there might also be preferences for certain educational or work paths. Example: In France, they seem to prefer profiles from the Grande École education system, while in Germany grades take higher importance than specific universities.
Demand-supply balance — countries might have an imbalance in supply and demand of applicants, making it at least statistically (and potentially perceptionally) harder or easier to land a job. Example: Switzerland is notoriously hard as a German or French speaker despite both speaking a local language, but the country is small and supply of applications is high; Middle East and Africa have had more demand for people than locally available in recent years, so a lot of foreigners landed jobs there (whether that lowered the barrier would be a heated discussion😉).
Different positions — there are roles and programs specific to a country. In some countries you can more easily find a job in consulting after just a bachelor's degree, while in others they require a master's — the difference is they offer entry roles at the respective level.
I would say in most cases you have the best odds in your home country as that's what most prefer, but there are exceptions in certain situations or countries where you might have a good chance.
Hence, for a more nuanced answer, we would have to look at your specific situation and the countries you consider.