Appending two dataframes with same columns, different order

You could also use pd.concat:

In [36]: pd.concat([noclickDF, clickDF], ignore_index=True)
Out[36]: 
   click    id  location
0      0   123       321
1      0  1543       432
2      1   421       123
3      1   436      1543

Under the hood, DataFrame.append calls pd.concat.
DataFrame.append has code for handling various types of input, such as Series, tuples, lists and dicts. If you pass it a DataFrame, it passes straight through to pd.concat, so using pd.concat is a bit more direct.