Question: My company has recently acquired another small company. Now, my company has a ERP system that we are using it presently. Also, the acquired company has an ERP system of its own. 

Now I have been given the responsibility of integrating my company's ERP System with the ERP system of the recently acquired company. To do this, I have to map the data between these two processes and see if there are any redundant features. 

However I was told by my friends that there would be lot of problems when I need to sit with both employees of the two companies, given the fact that my company doesn't treat the other company employees that well in terms of credibility. 

So I wanted to know, how do I make sure that there are no hard feelings between both sets of employees and what steps do I take for effective brainstorming sessions among both the teams?

Answer: 
You are in a very interesting situation. I agree with JMort on being assertive and making sure everyone knows you are responsible. 

Now, take in consideration that these two teams will continue to use the final result of your project after it is done (I assume they will not be fired), so you don't want to shut your chances of adoption. Think of the objectives of the project as the goal, but the road needs to set you up for success. 

Be objective and always ask, "why?" I find this question to work very well, even when you already know the answer. Together with, "how would you do it?" takes people from their defensive stand to a more communicative. I often find people complaining without possible alternative solutions, making them more friends of your proposition.

Be open, and open for feedback, but always keep control. **Make sure from the beginning that you say that you will be collaborative, but if there is any tie-breaking you will make that call.** 

As a final point, try to watch for the influencers in both teams, infiltrate them, convince them, and win them. This will make your life much easier.
Bring pizza or cookies to the kickoff/first meeting. Talk about the culture, the takeover, and other elephants in the room. Try to find common ground and common goals. If you can accomplish that in the first meeting you've accomplished a lot. 

If nothing else, tell them this will look good on your resume, too. Let them know you didn't personally commit the takeover, etc. In other words, you need to establish a trusted relationship before you can expect cooperation. It will take time - but people come around quickly in these situations, especially in bad economic times.
Good luck.