What are the Pros/Cons of investing in the Bitcoin ETF vs. bitcoins yourself? Hypothetically, the Winklevoss ETF is approved tomorrow, 3/10/17. The ETF price, which starts at $100/share, will correlate directly with the price of Bitcoin, I assume. What would be some pros/cons of investing in the ETF instead of buying bitcoins myself and storing them in my own wallet? The ETF would be easier to buy/sell than using an exchange plus I wouldn't have to worry about the security of my coins.
When you say "I won't have to worry about the security of my coins"... I think you've got this backward.

There's nothing more secure than a paper wallet that has been generated offline. Bitcoin was created as a way to avoid the need to trust a third party. If you don't believe that's necessary, then you're just trading it hoping to make USDs, not because you believe in it's intrinsic value.

in other words,

Are you speculating on the price, short term, hoping to make USD?

Get the ETF.

Are you skeptical of the global financial system, and want to hold money outside the reach of any government?

Hold bitcoin.