I have a seven year old studying in India and now I will have to move to Krakow for 2-3 years.
I would suggest the BISC (British school) for a couple of reasons.
Firstly, you are from India so the British education system will be more familiar to you as your own education system is based on it. The main difference is that the modern British system allows more creativity and practical work rather than just rote learning and theory.
Secondly, the British School in Krakow follows the British National Curriculum, so you know exactly what your child will be learning down to the last detail. The national curriculum sets a standard for course content and expected attainment for children. For example your child at age 7 + will be in Key Stage 2 of the curriculum.
The National Curriculum sets out what children in KS2 should be taught. There are 11 mandatory subjects:
Ancient and modern foreign languages
Art and design
Design and technology
Physical education (which must include swimming)
Computing (often called information and communication technology or ICT)
At the end of Key Stage 2 your child will be tested:
Key stage 2: English grammar, punctuation and spelling test framework
Key stage 2: English reading test framework
Key stage 2: mathematics test framework
Key stage 2: science sampling test framework
Test scores are published online so parents can compare their children's scores with the national average.
The USA does not have a national curriculum so the American school in Krakow designs its own curriculum and sets its own standards based loosely on different curricula:For our core courses, we draw on standards from the Common Core, American Education Reaches Out (AERO), and Next Generation Science Standards. For our languages, arts, and physical and health education program, we draw on additional standards from the province of Ontario, and from the national curricula of Poland and France.
As you can see that's quite a mixed bag and it takes great skill to deliver such a curriculum effectively and ensure standards. They also don't have any standardized testing system.
As a teacher myself and having taught many children from India over a number of years :) I understand how important it is for Indian parents abroad to keep their children up to the high standard they will need to maintain if they re-enter the Indian education system later on. I know that very high standards in English literacy are required from quite young children in India so I would opt for the British school if you can afford it, as your child will definitely get a thorough grounding in language and maths.