Intruder one
If you are a foreign employee on a work visa (H1 or L1) in the USA you have to pay all the taxes as a citizen and can avail of all the standard deductions as a citizen. You get back a portion of your taxes and not all your taxes in the USA based on your deductions you make and file at the end of the year. No different and often times get no benefit for your Social security and medicare benefit if you do not convert to a citizen and therefore lose all that.
If you are a foreigner in India on a work visa you have to pay all the taxes of an Indian citizen and you can avail of all the deductions and options available to an Indian Citizen. Difference being that the company structures it for you into your payroll so that you don't have to do the running around end of the year (as described by Hi Flyer787) and therefore instead of getting a refund at the end of the year from the Indian Govt you get a smaller deduction on your pay check every month and therefore more cash in hand. $13000 as per HIflyer will bring you about $11,000 in hand post taxes.... I am assuming the same in the USA or less?
I am sure based on the Double taxation treaty the US will therefore not allow you to claim deductions twice. However if in addition to those expenses you are claiming in India you have more expenses stateside and are eligible for more rebates I am sure you can claim them. The US embassy here is very helpful with guidance on this matter.
AS in my first post I therefore recommend a tax consultant to structure this to ensure you get the best deal.
Many ex pat aviators and workers in India and if you browse the forum I have yet to come across a topic where they have an issue on taxation.....other issues abound but then that is a personal opinion.