Welcome to the forum!
You may want to click on the tags below and read some threads to get a feel for the two churches.
Other than that, about the only advice I can give is to wear white, or at least very light colors, when you go to the Ethiopian Church, as that is their custom. Also, if you are female (it's hard to tell on the internet
) when visiting either church, you may want to take along a scarf or mantilla, as head coverings tend to be more commonly used in OO churches than in other churches. Other than that, you should be fine as long as you are respectful, which I'm sure you will be.
There are not any doctrinal differences, since both churches are OO. You may want to call ahead and see if either have English liturgies. I seem to think that may be more likely in the Indian church, but I could be wrong. If you want to get a feel for the worship of either church, you may want to click onto the Oriental Orthodox music thread, which is a sticky at the top of the OO forum.
I hope you have a good experience. Please let us know what happens.