how does robo studio and gazebo differ?

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I'd say that the main difference is that Gazebo is a fully-fledged, open world, general purpose dynamic simulator that is integrated / can be used with ROS on multiple levels, while ABB RobotStudio is primarily designed to simulate (parts of) industrial work cells with ABB robots in them, and can only be interacted with (from ROS) through packages like abb_driver.

This means Gazebo will also simulate the physics of any objects not your robot, while I believe RobotStudio does just enough dynamics to guestimate the cycle times of a robot in a particular environment, running a particular program.

However, RobotStudio will very likely be (much) better at simulating ABB robots, seeing as it was created by the manufacturer of those robots, and I would expect them to be experts when it comes to their own products. It also provides a faithful simulation/emulation of the controller hardware, its software and the interfaces to it, something Gazebo obviously doesn't do.

i am actually looking to simulate obstacle avoidance for an ABB serial manipulator with 6 DOF.

In general I'd say that you can use RobotStudio if the dynamics of your simulation do not matter and your environment is static. ROS (I assume you'll want to use MoveIt) will need sensor data (ie: rgbd, lidar, etc) if you need dynamic obstacle avoidance or have a planning scene which changes over time, which afaik RobotStudio will not be able to provide (but do look into that, as it has been a while since I last used it). For those cases, I'd use Gazebo, as it is already fully integrated with ROS, both on the sensor, as well as the actuation side.