BTC denominated vs fiat denominated stock exchange? What could be done more easily (or just be doable) in a BTC-denominated stock exchange that is difficult (or plain impossible) in a fiat-denominated one?

i.e. what features of a BTC denominated exchange would make it relatively attractive to ordinary traders?
Advantages of BTC stock exchanges

1) Speed of deposits and withdrawals

Ordinary investors (in USA where there is no SEPA) use ACH transfers or checks to fund their brokerage accounts. ACH transfers take 3 business days and make no progress on the weekends. After this is in the brokerage account it takes another 3 days for the cash to "settle". So in an extreme case where there is a holiday weekend, a money transfer to a stock exchange (with the intent to buy stock based on new time sensitive information) on a Thursday will take

(1) Friday, (1) Saturday, (1) Sunday, (1) Holiday Monday, (2), Tuesday, (3) Wednesday, (1-Settle) Thursday , (2-Settle) Friday, (2-Settle) Saturday, (2-Settle) Sunday, (3-Settle) Monday, (Tradeable) Tuesday

On Software as a Service bitcoin denominated stock exchanges (this is also known as "centralized") this takes just a few confirmations which will average an thirty minutes (3 confirmations) to an hour (6 confirmations) to fund an account, and the bitcoin is immediately then available for trading. For trades requiring less time to profit, the user can limit exchange risk by withdrawing their bitcoin from an exchange when they are not using it, and this only takes another the time for it to confirm to their personal addresses. Using ACH transfer from a fiat exchange will again require 3 business day cash settlement time (for stock sells, derivatives have 1 business day cash settlement time) and an additional 3 business days to reach their actual bank account. 

If this investor is using a check from the brokerage, the time is further compounded by an 3 business days in snail mail.

But Wire/SWIFT transfers obviously aren't much better, due to the cash settlement time before the transfer happens.

On a decentralized exchange (using mastercoin protocol, counterparty, or colored coins), one does not need to "deposit" bitcoin at all, but the sacrifice being the stock trades themselves are at the mercy of the confirmation speed, so many kinds of trading (time sensitive under 30 minutes) are not practical, but investing and swing trading is. Colored Coin protocol does not have this sacrifice. On decentralized exchanges AML is impossible barring some future invention that attempts to make some bitcoin tainted to the entire network.

2) More liquid and greater fungibility: Investment funds can be spent for goods and services, indistinct from a personal wallet's funds.

On fiat stock exchanges, brokerages create investment accounts where cash has to "settle" and be transferred to a bank account before it can be spent on goods and services. We have already established that this can take two weeks.

On bitcoin exchanges, the user's exchange addresses (accounts) are indistinct from their personal accounts. On the centralized exchanges, they function as hosted wallets, if userA wants to get paid to a bitcoin address, userB doesn't know if the requested address is being accessed on bitcoin-QT or tied to an account on a stock exchange. Similarly if userA wants to send funds from a stock exchange they can simply 'withdraw' it to userB's requested address.

On decentralized exchanges, once again the user's funds have never left their private wallet to begin with and there is no concept of withdrawing before money can be spent on goods and services.

3) Economic freedom. Invest in companies in any jurisdiction in the world, and for-profit decentralized services that have no jurisdiction.

In fiat stock markets, a company has to list in each individual market in each individual country, and investors outside of those markets/countries cannot invest. (If an investor has practical access to invest in foreign stock markets, they are not your ordinary investor). Also many markets and countries have capital controls as well as socioeconomic barriers to entry.

In bitcoin stock exchanges, these barriers do not exist. If you want to invest in a hot sector in Gangzhou China or Missouri USA, you can just do that. On centralized exchanges, site operators have at some points attempted to limit people from certain countries (america) from accessing their markets, due to liability issues. With decentralized exchanges there is no practical way to limit access in this way.

4) Low to nonexistent costs to listing a company.
Many more types of crowdfunding can take place since hundreds of thousands of dollars in legals fees are not necessary to create an asset for trading.

5) Smaller investors can invest.
In fiat stock exchanges, minimum funding requirements can be $2,000 for a margin account or minimum account size at all. Its fun to tell teenagers to invest $100 a week in a stock so they'll be rich by the time they are 50, but no decent brokerage will let them open an account, and they'll be better off trading Nike shoes and go on to other frivolous activities.

In bitcoin stock exchanges this doesn't exist. Some centralized exchanges have high fees to enter, decentralized exchanges cannot barring a future protocol that does.

6) Lower fees to trade.
centralized exchanges have their own trading fees. decentralized exchanges will only have the network fee and whatever their protocol requires.

fiat stock market fees can be much higher, at 'discount brokerages', in direct access markets, and in tailored investment firms (bucket shops)

7) Data feeds are not delayed, free
Fiat stock markets give delayed data unless the investor goes out of their way to find better and better data with more and more custom tailored services. It is only a fairly recent change that an individual investor can get live quotes across exchanges at all, let alone level 2 order book information. But even then, this investor has to do a lot of research to find ways to do this cheaply.

No bitcoin stock exchange delays data. This would actually be hard to do. This is impossible on decentralized exchanges and no centralized exchange would gain a community if they did that.

8) Free API access
In fiat stock markets, getting API access to data feeds is impossible or very expensive. Nasdaq charges $6,000 a month for this access, and the protocol (FIX) is very antiquated compared to JSON and restful services.

Bitcoin stock exchanges all user modern JSON, some use various forms of restful services and Oauth. All provide this for free, not as a courtesy but because that is modern and the data is there.

Now ordinary investors are able to both VIEW live data and retrieve it via API for their own applications.

With fiat stock exchanges, making trading applications such as automated bots were largely out of reach for ordinary investors due to the restrictions in data access, contributing to an illusion that "High Frequency Trading" was an unattainable mystical trade reserved for the mystical quantitative programmers in secretive hedge funds.

9) 24/7 market hours

Bitcoin stock exchanges never close. Trade any asset any hour of the day. There are no gap ups and gap downs due to information coming out while markets were closed.

This is an advantage because information can become available at any time for a security in any part of the world.

In centralized exchanges, implementing "closed" hours is difficult (but a future exchange may opt to do this), and in decentralized exchanges this is impossible barring some future protocol change.

Advantage of fiat stock exchanges

1) Margin, lots and lots of margin. bitcoin currently does not have a practical way to offer margin for stocks.

2) SIPC insurance, for stocks. If the exchange shuts down many regulatory environments have a way for depositors to get their money back up to a point.