Taking pure term insurance from an organization other than LIC?

I am looking for a term insurance cover. I have been doing some preliminary research and what I observed is that LIC of India’s premium is higher by at least 25% as against its competition. I was quoted Rs. 33,850 for their “Amulya Jeevan” policy with a cover of Rs. 50 lakhs whereas ICICI Prudential has quoted only Rs. 25,144 that includes a few riders (no riders whatsoever with LIC). My questions are:
1. Why is there so much of price difference between the products. Should LIC not be cheaper owing to their operating style and size?;
2. Can I go ahead and take the cover from any company that offers lowest rates without fearing any issues related to claim settlement? Agents from both sides (LIC and others) have shown the tendency to disparage the others products/image and I am not able to make up my mind based on their advise.