You have to draw a distinction between the two browsers you mentioned. Both Avant and Orca are developed by the same software team, headed by a Chinese programmer named Anderson Che.
Orca Browser is a web browser based on the Firefox (3) core with the same speed and features of Firefox in addition to a handful of extra features.
Avant Browser was largely inspired by Opera and wrapped the layout engine used by Internet Explorer.
No browser is impervious to security problems, although all the developers and programmers involved with the development of these browsers are obviously working continuously to reduce vulnerability of their products.
Ultimately the choice of a browser comes down to personal preferences coupled with a bit of common sense regarding, amongst other factors, security issues. Here is a link to a recent browser security test results summary for you to have a look at. http://nsslabs.com/test-reports/Q309...mary_Final.pdf
Hope this helps.