BUG: series.eq(other) does not equal series == other when the series contain pd.NA
- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
# Using pd.NA:
>>> import pandas as pd
>>> df = pd.DataFrame(data=[[1, 1], [2, 2], [3, 3], [pd.NA, pd.NA]], columns=['a','b'])
>>> df.a == df.b
0     True
1     True
2     True
3    False
dtype: bool
>>> df.a.eq(df.b)
0    False
1    False
2    False
3    False
dtype: bool

# Using np.nan instead of pd.NA:
>>> import numpy as np
>>> df_np = pd.DataFrame(data=[[1, 1], [2, 2], [3, 3], [np.nan, np.nan]], columns=['a','b'])
>>> df_np.a.eq(df_np.b)
0     True
1     True
2     True
3    False
dtype: bool
```

#### Problem description

From the [documentation](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.eq.html#pandas.Series.eq) of `Series.eq`: "Equivalent to `series == other`", I would expect `df.a == df.b` to yield the same result as `df.a.eq(df.b)`, but it doesn't when the series contain `pd.NA`.

#### Expected Output
`df.a.eq(df.b)` gives the same result as `df.a == df.b` even when the series contain `pd.NA`.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : db08276bc116c438d3fdee492026f8223584c477
python           : 3.8.5.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.4.0-48-generic
Version          : #52-Ubuntu SMP Thu Sep 10 10:58:49 UTC 2020
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.1.3
numpy            : 1.19.1
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.2.1
setuptools       : 49.2.1.post20200802
Cython           : None
pytest           : 6.0.1
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : 1.3.1
lxml.etree       : 4.5.1
html5lib         : None
pymysql          : 0.10.0
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.15.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : 0.7.4
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.0
numexpr          : None
odfpy            : None
openpyxl         : 3.0.4
pandas_gbq       : None
pyarrow          : 1.0.0
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.2
sqlalchemy       : 1.3.18
tables           : None
tabulate         : 0.8.7
xarray           : 0.15.1
xlrd             : 1.2.0
xlwt             : None
numba            : 0.48.0

</details>
