In answering this question it is important to understand the way in which these two countries and the people that are in them are used as symbols of various aspects of mankind and being human. The people that you will pick will depend a lot on which of these symbols you find less offensive to your own version of humanity.
I would never choose to be a Lilliputian, for example, because their diminished stature clearly shows the way in which mankind has such pride and arrogance in an existence that is actually incredibly puny and small when it comes down to it. There is tremendous irony in the Lilliputians and the way that they are presented as the most arrogant and vainglorious race that Gulliver comes across, and Skyresh is of course the most arrogant character in the entire novel.
The Brobdingnags, on the other hand, are used to symbolise the private sphere of human life that Gulliver, because of his small size, is privy to. He is treated much like a doll in this country, and therefore sees "normal" activities such as defaecation and sexual activity that it is not normal to see. Whilst descriptions of the stench and excrement of these people clearly show that they are satirised as well, at the same time, Brobdingnags are shown to be noble people as the queen's kindness towards Gulliver demonstrates. They symbolise therefore what human life is like through the microscope as it were. If I had to pick one of these people, I would therefore choose to be a Brobdingnag because they have at least the option to be noble rather than the Lilliputians, who are shown to be arrogant through and through.