Oh! Sorry I think this is an unreported bug in longtable.
Longtable inserts a strut to keep a minimal separation between the text and any \hline or the previous row.
It does this with the following code
\def\LT@startpbox#1{%
\bgroup
\let\@footnotetext\LT@p@ftntext
\setlength\hsize{#1}%
\@arrayparboxrestore
\vrule \@height \ht\@arstrutbox \@width \z@}
If you look at the equivalent code in the array package, you find
\def\@startpbox#1{\bgroup
% \end{macrocode}
% The argument is the width of the box. This information has to be
% assigned to =\hsize=.
% Then we assain default values to several parameters used in a
% \textsf{parbox}.
% \changes{v2.3k}{1998/05/12}{Use \cs{setlength} to set \cs{hsize},
% so that the calc package can be applied here (pr/2793)}
% \begin{macrocode}
\setlength\hsize{#1}\@arrayparboxrestore
% \end{macrocode}
% Our main problem is to obtain the same distance between succeeding
% lines of the \textsf{parbox}.
% We have to remember that the distance between two \textsf{parboxes}
% should be defined by =\@arstrut=. That means that it can be
% greater than the distance in a \textsf{parbox}.
% Therefore it is not enough to set a =\@arstrut= at the
% beginning and at the end of the \textsf{parbox}. This would
% dimension the distance
% between first and second line and the distance between the two
% last lines of the \textsf{parbox} wrongly.
% To prevent this we set an invisible rule of height
% =\@arstrutbox=
% at the beginning of the \textsf{parbox}. This has no effect on the
% depth of the first line. At the end of the \textsf{parbox} we set
% analogously another invisible rule which only affects the depth
% of the last line. It is necessary to wait inserting this strut
% until the paragraph actually starts to allow for things like
% =\parindent= changes via =>{...}=.
% \changes{v2.1c}{1992/12/14}{Use `everypar to insert strut}
% \begin{macrocode}
\everypar{%
\vrule \@height \ht\@arstrutbox \@width \z@
\everypar{}}%
}
% \end{macrocode}
% \end{macro}
The important bit being the last few lines which delay adding the strut by using \everypar.
It seems to me the same fix should have been applied to longtable so only 20 years too late I suggest
\def\LT@startpbox#1{%
\bgroup
\color@begingroup% Omit line if package date older than 2014/10/28
\let\@footnotetext\LT@p@ftntext
\setlength\hsize{#1}%
\@arrayparboxrestore
\everypar{%
\vrule \@height \ht\@arstrutbox \@width \z@
\everypar{}}%
% \vrule \@height \ht\@arstrutbox \@width \z@
}
which then makes both your tables have the same vertical spacing.
If you do this could you change
\ProvidesPackage{longtable}
[2004/02/01 v4.11 Multi-page Table package (DPC)]
to
\ProvidesPackage{longtable}
[2004/02/01 v4.11 Multi-page Table package (DPC) + strut fix]
I suspect after all this time I can't change longtables default spacing, however I should add an option to fix it.
You should use split inside equation for this:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
\pi^{(1)}_{i j}
={}& -\frac{1}{4}\eta^{\lambda \sigma} ( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha} ) \biggl\{ \frac{1}{2}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) \biggr\} \partial_{\sigma} h_{\alpha \beta}
\\
& -\frac{1}{4}\eta^{\lambda \sigma} ( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha} ) \biggl\{ \frac{1}{2}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} ) \biggr\} \partial_{\lambda} h_{\mu \nu}
\\
={}& -\frac{1}{4}\partial^{\lambda} h^{\mu \nu}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) -\frac{1}{4}\partial^{\sigma} h^{\alpha \beta}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} )
\\
={}& -\frac{1}{2}\partial^0 h^{i j} - \frac{1}{2}\partial^0 h^{i j}
\\
={}& \dot{h}_{i j}
\end{split}
\end{equation}
\end{document}
The trick is to put = on the left side, following it with {} for ensuring correct spacing.
Avoid useless \left and \right. Also, no \enspace should be used around =.
The number should go in the middle, in my opinion. However, the tbtags option to amsmath will put it at the bottom of a split.
Best Answer
For one-off spacing changes,
\smallskip,\medskip, and\bigskipare defined for this task.After rereading the question, I'll note that these aren't 'fixed' spaces; they're rubber lengths (defined according to
\smallskipamount, etc.) and will shrink/expand according to the amount of available vertical space when the page is being built.