BUG: DatetimeIndex.equals returns false if units mismatch

[batterseapower]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

assert pd.DatetimeIndex(['2020-01-01'], dtype='datetime64[s]').equals(
    pd.DatetimeIndex(['2020-01-01'], dtype='datetime64[ns]')
)

Issue Description

This assertion should pass, but it fails.

Expected Behavior

The assertion should pass for the same reason that this one does:

assert pd.Index([0, 1], dtype=int).equals(pd.Index([0., 1.], dtype=float))

Or that this one does:

assert np.array_equal(
    pd.DatetimeIndex(['2020-01-01'], dtype='datetime64[s]').values,
    pd.DatetimeIndex(['2020-01-01'], dtype='datetime64[ns]').values
)

Installed Versions

INSTALLED VERSIONS ------------------ commit : e86ed37 python : 3.10.10.final.0 python-bits : 64 OS : Linux OS-release : 4.18.0-348.20.1.el8_5.x86_64 Version : #1 SMP Thu Mar 10 20:59:28 UTC 2022 machine : x86_64 processor : x86_64 byteorder : little LC_ALL : None LANG : en_GB.UTF-8 LOCALE : en_GB.UTF-8

pandas : 2.1.1
numpy : 1.23.5
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.7.2
pip : 23.1.2
Cython : 3.0.0
pytest : 7.3.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.9.2
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.13.2
pandas_datareader : None
bs4 : 4.12.2
bottleneck : 1.3.7
dataframe-api-compat: None
fastparquet : None
fsspec : 2023.6.0
gcsfs : None
matplotlib : 3.7.1
numba : 0.56.4
numexpr : 2.8.7
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 10.0.1
pyreadstat : None
pyxlsb : None
s3fs : 2023.6.0
scipy : 1.10.1
sqlalchemy : None
tables : None
tabulate : None
xarray : 2023.4.2
xlrd : 2.0.1
zstandard : None
tzdata : 2023.3
qtpy : 2.3.1
pyqt5 : None

[ziadk]

I think this is related to this issue #55564

[paulreece]

Confirmed. Exists on main and 2.1.x.

[jbrockmendel]

Not related to #55564, but it is related to #55638 and #33940. 33940 is probably a good place to comment if you have an opinion here.

[avm19]

This behaviour is not limited to pd.DatetimeIndex, but also applies to pd.Series and pd.Dataframe. At least in version 2.0.3.