Civilian droids like protocol droids, I can see the importance of possessing sentient-like personalities. In military droids where intelligence is necessary, such as assassin or tactical droids, I can agree that a personality may potentially improve performance, but what real use is a personality in your everyday battle droid, whose only need for intelligence is to distinguish friend from foe and accurately carry out orders without question?
As Galactic Basic is essentially Earth English, and therefore can be quite confusing, having a personable AI could prove to enhance comprehension of orders.
HK47 is a fine example of a droid that understood the deficiencies of obeying "meatbags". Astromechs also have a verbose personality, and yet lack ability to communicate in Basic back to their living counterparts. While not strictly military, they do serve that capacity in a limited sense. It makes them easier (excepting R2) to deal with. Everyone in the Trade Federation seemed rather paranoid, having a personality that was submissive may have given an bloated sense of power. We may not ever know for certain though.
I answered (what I think is) a similar question here. The gist of it being that ontop of their basic intelligence, they were given more and more data to process and this overloaded their abilities. In attempting to resolve this, it led to them manifesting the appearance of (individual) personality.
We are seeing the answer to this question in real life today. I just read an article where Google fed movie dialog to their neural net and were surprised to find that it can carry on a realistic conversation with people. Now, from this, you can extrapolate that even the common soldier battle droid would need to communicate with humanoid Generals in an easy intuitive way and follow the spirit and letter of the orders. Some machine that is limited would require a programmer to set the parameters of the orders. This is basically my day to day job. I get paid a lot of money because people cannot tell a limited computer what they want it to do! So in conclusion... Google is working to make me unemployed