designed by Jon Kabat Zinn... the Vipassana technique of awareness-based body scans...I have done S.N.Goenkya's ten days meditation courses
Awareness-based body scans in themselves are not "vipassana". It appears Jon Kabat Zinn & S.N.Goenkya have simply hijacked or misappropriated the word "vipassana".
The word "vipassana" means "clear seeing" and does not mean any specific method of tracking a meditation object.
While it is possible awareness-based body scans may result in "vipassana" happening, awareness-based body scans in themselves are not "vipassana".
In summary, there is no record of the Buddha ever teaching awareness-based body scans.
I currently follow Ajahn Brahm's meditation guide book Mindfulness
Bliss and Beyond. When I told my friend who didn't know about Ajahn
Brahm, he said 'his teacher said that calming the mind is a wrong
technique of meditation'.
Ajahn Brahm's book emphasizes "jhanas", which are the final component of the Buddha's Noble Eightfold Path. Ajahn Brahm's book also correctly refers to "insight/vipassana based on jhana" (p 223), quoting the sutta MN 43.
Ajahn Brahm's book quotes & teaches a method of practise the same as the Lord Buddha taught from SN 48.9 (which is also taught at the very end of the Anapanasati Sutta), namely, making "letting go (vossagga)" the meditation object.
Now when I look at it, S.N Goenka's Vipassana technique though good
for healing the subconscious mind does not talk about reaching higher
meditative absorption of Jhanas.
S.N Goenka's technique is unrelated to "vipassana". If S.N Goenka's technique resulted in "vipasssana" then "jhanas" would arise from that vipassana because the Pali suttas say jhanas & wisdom develop eachother, as follows:
Natthi jhānaṃ apaññassa, paññā natthi ajhāyato ; Yamhi jhānañca paññā
ca, sa ve nibbānasantike.
There is no meditative concentration for him who lacks insight, and no insight for him who lacks meditative concentration. He in whom
are found both meditative concentration and insight, indeed, is close
Whereas Ajahn Brahm, in his book and in his youtube videos talk about reaching Nimmitas and Jhana through Anapanasati i.e. Breath Awareness Meditation.
The Buddha practised & taught Anapanasati. Refer to SN 54.11 & MN 118.
Which is the right way to go?
The Buddha taught Anapanasati.
What is the difference between Vipassana and Anapanasati goals of attainment?
Anapanasati practised correctly results in vipassana. Anapanasati describes 16 sequential experiences/steps and vipassana begins to occur at the 3rd step, which is called 'experiencing all bodies' (refer to this book), which means experiencing how the quality of the mind conditions the quality of the breath and the body, which is an insight into the Four Noble Truths.
In addition, if anapanasati is practised correctly (with a clear mind established in letting go), the impermanence, unsatisfactoriness & not-self of the breathing is also seen starting at step 3.
Each of the four tetrads of Anapanasati includes "vipassana". The 4th tetrad of Anapanasati is exclusively vipassana. Try to ignore those who have not fulfilled the training; when they say false things, such as: "Samatha tetrads 1 to 3 and Vipassana tetrad 4".
In the Anapanasati Sutta, each step (except steps 1 & 2) is preceded by the instruction: "He trains himself". This means the practitioner is developing the Three Trainings of higher morality, higher mind & higher wisdom, therefore, developing vipassana in each step starting at step 3.
Can I attain Nirvana without doing Vipassana but by just doing Anapanasati?
Anapanasati is vipassana. The teachings of Jon Kabat Zinn & S.N.Goenkya are not necessarily vipassana. If they were, you would be already enlightened.
Is there a difference between Vipassana Jhana and Anapanasati Jhana?
The above terms are invalid and unrelated to what the Buddha taught.