There are several discussions about phishing and socially engineered malware attacks, I found an article that help to understand how browsers are ready to detect these attacks.
Take a look on the report published on NSS Labs "Q3 2099 Phishing Test Report", This report examines the ability to protect users across the following browsers  :

• Apple Safari v4
• Google Chrome 2
• Microsoft Internet Explorer v8
• Mozilla Firefox v3
• Opera 10 Beta

Extract from NSS Labs Blog :
Socially engineered malware is the most common and impactful threat on the Internet today, with browser protection averaging between 1% and 81%. Internet Explorer 8 caught 81% of the socially engineered malware sites over time, leading other browsers by a 54% margin. Safari 4 and Firefox 3 caught 21% and 27% respectively, while Chrome 2 blocked 7% and Opera 10 Beta blocked 1%.

Phishing protection over time varied greatly between 2% and 83% among the browsers. Statistically, Internet Explorer 8 at 83% and Firefox 3 at 80% had a two-way tie for first, given the margin of error of 3.6%. Opera 10 Beta, exhibited more extreme variances during testing and averaged 54% protection. Chrome 2 consistently blocked 26% of phishing sites, and Safari 4 offered just 2% overall protection. Firefox 3.5 crashing issues prevented it from being tested reliably.

The Report can be read here : Phishing Test Report(PDF File)