His concern is that the large companies might be more likely to get it.
Is that true at all?
I tried to google this but didn't find any substantial evidence.
Once the application is selected in the lottery, USCIS will start looking at the background of the company and if it's a legit corporation.
"Only" if you are going through one of the shady Indian consultancy(+) companies in the bay area, their is a chance they will want to probe more and might reject your application. But like you said it's a startup with a product, you should be fine with either choice, and I would not worry too much if I were you.
(+)These are basically companies that will apply for an H1B for a fee (H1B + their own commission) but they don't really have a product or a job for you. If the application is accepted, you can either find a job on your own and transfer your H1B AND/OR they will try to place you in some company and take a commission out of your salary.