The subset of people who need privacy can use both in a manner that achieves it.
If TPTB close off the ability to get an anonymous connection to the internet (e.g. public open WiFi and/or unregistered 3G USB dongles), then neither Monero nor Bitcoin can be used anonymous any more.
They are likely to pass regulations banning those in next few years. I have seen legislation and movements by the telcos and ISPs.
You could I guess rent a botnet to obfuscate your IP. But much better we fix Tor or I2P (if they are compromised by Sybil attack and timing analysis as I posit they are).
Bitcoin's lack of onchain anonymity means it is nearly impossible to maintain anonymity in any sane usage scenarios. Do we need to detail why? Hasn't this been explained already in Monero threads?
Also I think you are assuming that anonymity will be a rare usage scenario; whereas, I am think it will be normal one in the Knowledge Age.
Regarding "better mining algo", again this is not a property of money I think people who are resorting to these types of arguments to convince themselves that altcoin x is better are kidding themselves.
When Bitcoin is centralized and fully regulated you can appreciate that the mining algorithm goes hand-in-hand with driving the freedom that makes money.