Not all applys are alike

The below chart suggests when to consider apply¹. Green means possibly efficient; red avoid.

Some of this is intuitive: pd.Series.apply is a Python-level row-wise loop, ditto pd.DataFrame.apply row-wise (axis=1). The misuses of these are many and wide-ranging. The other post deals with them in more depth. Popular solutions are to use vectorised methods, list comprehensions (assumes clean data), or efficient tools such as the pd.DataFrame constructor (e.g. to avoid apply(pd.Series)).

If you are using pd.DataFrame.apply row-wise, specifying raw=True (where possible) is often beneficial. At this stage, numba is usually a better choice.

GroupBy.apply: generally favoured

Repeating groupby operations to avoid apply will hurt performance. GroupBy.apply is usually fine here, provided the methods you use in your custom function are themselves vectorised. Sometimes there is no native Pandas method for a groupwise aggregation you wish to apply. In this case, for a small number of groups apply with a custom function may still offer reasonable performance.

pd.DataFrame.apply column-wise: a mixed bag

pd.DataFrame.apply column-wise (axis=0) is an interesting case. For a small number of rows versus a large number of columns, it's almost always expensive. For a large number of rows relative to columns, the more common case, you may sometimes see significant performance improvements using apply:

# Python 3.7, Pandas 0.23.4
np.random.seed(0)
df = pd.DataFrame(np.random.random((10**7, 3)))     # Scenario_1, many rows
df = pd.DataFrame(np.random.random((10**4, 10**3))) # Scenario_2, many columns

                                               # Scenario_1  | Scenario_2
%timeit df.sum()                               # 800 ms      | 109 ms
%timeit df.apply(pd.Series.sum)                # 568 ms      | 325 ms

%timeit df.max() - df.min()                    # 1.63 s      | 314 ms
%timeit df.apply(lambda x: x.max() - x.min())  # 838 ms      | 473 ms

%timeit df.mean()                              # 108 ms      | 94.4 ms
%timeit df.apply(pd.Series.mean)               # 276 ms      | 233 ms

¹ There are exceptions, but these are usually marginal or uncommon. A couple of examples:

1. df['col'].apply(str) may slightly outperform df['col'].astype(str).
2. df.apply(pd.to_datetime) working on strings doesn't scale well with rows versus a regular for loop.

For axis=1 (i.e. row-wise functions) then you can just use the following function in lieu of apply. I wonder why this isn't the pandas behavior. (Untested with compound indexes, but it does appear to be much faster than apply)

def faster_df_apply(df, func):
    cols = list(df.columns)
    data, index = [], []
    for row in df.itertuples(index=True):
        row_dict = {f:v for f,v in zip(cols, row[1:])}
        data.append(func(row_dict))
        index.append(row[0])
    return pd.Series(data, index=index)