At the outset, let me make it clear that you should not equate both the Acts. Both are different in terms of benefits, administrative authorities, manner of compliance, etc. You are right, an employee and employer need to contribute under the ESIC scheme to avail the facilities. However, remember that one cannot choose between the Acts.
Employee's Compensation Act 1923
The Employee's Compensation Act 1923 (previously known as the Workmen's Compensation Act 1923) is applicable only where the ESI scheme is not implemented. The Employee's Compensation Act 1923 does not require either the employee or the employer to contribute. First, you have to examine whether the Act is applicable to your organization. Section 2(1)(dd) defines an employee, and there is a Schedule II annexed to the Act specifying who is considered an employee. Section 3 of the Act stipulates that if personal injury is caused to an employee by an accident arising out of and in the course of his employment, his employer shall be liable to pay compensation in accordance with the provisions of Chapter II of the Act.
I hope I have been able to clear your doubt.
Regards,
BS Kalsi