I don't know how it will affect size, but native .ai files generally work better than .eps when placed in ID.
EPS files don't support transparency. At least on a Mac, it's more difficult to get a good preview sometimes.
The AI format supports all the features in Illustrator, and when you place an AI file, you can choose what layer(s) to place and what artboards.
Don't use EPS anymore as it does not support transparency or color management. Use either AI or better PDF/X-4 to place in InDesign.