Amazing improvement of script execution speed when split - not understood
Your comment confirms that the original long script was using variables and these have become parameters.

Probably you are benefitting from parameter sniffing here and better execution plans. The values for variables are not sniffed unless you use the ’option recompile' query hint so you will get the same plan regardless of what the runtime values are.

When you parameterize it SQL Server sniffs the parameter value at the time the plan for the statement is actually compiled and can look in the column statistics using these actual values. Based on that you can get hopefully better row estimates and a more suitable plan.

As a side note parameter sniffing can have its own problems if the plan is cached and the procedure is executed again with a different parameter value as the original plan might not be optimal for the new parameter value.