With the following code:
\documentclass[a4paper]{report}
\usepackage{lipsum}
\begin{document}
a
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Ord & Esplicito (Adam-Bashforth) & Implicito (Adam-Moulton) \\\hline
0 & & $y_{n+1}=y_n+hf_{n+1}$ Eulero implicito \\\hline
1 & $y_{n+1}=y_n+hf_n$, Eulero esplicito & $y_{n+1}=y_n+\frac{h}{2}(f_{n+1}+f_n)$ Greg-Nickolson \\\hline
2 & $y_{n+1}=y_n+\frac{h}{2}(2f_n-f_{n-1})$ & $y_{n+1}=y_n+\frac{h}{12}(5f_{n+1}+8f_n-f_{n-1})$ \\\hline
3 & $y_{n+1}=y_n+\frac{h}{12}(23f_n-16f_{n-1}+5f_{n-2})$ & \\\hline
\end{tabular}
\end{center}
\lipsum[1]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Ord & Esplicito (Adam-Bashforth) & Implicito (Adam-Moulton) \\\hline
0 & & $y_{n+1}=y_n+hf_{n+1}$ Eulero implicito \\\hline
2 & $y_{n+1}=y_n+\frac{h}{2}(2f_n-f_{n-1})$ & $y_{n+1}=y_n+\frac{h}{12}(5f_{n+1}+8f_n-f_{n-1})$ \\\hline
3 & $y_{n+1}=y_n+\frac{h}{12}(23f_n-16f_{n-1}+5f_{n-2})$ & \\\hline
\end{tabular}
\end{center}
b
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Ord & Esplicito (Adam-Bashforth) & Implicito (Adam-Moulton) \\\hline
0 & & $y_{n+1}=y_n+hf_{n+1}$ Eulero implicito \\\hline
2 & $y_{n+1}=y_n+\frac{h}{2}(2f_n-f_{n-1})$ & $y_{n+1}=y_n+\frac{h}{12}(5f_{n+1}+8f_n-f_{n-1})$ \\\hline
\end{tabular}
\end{center}
c
\end{document}
I get:

The examples make me suspect the greater vertical space, which is what troubles me, is due to the overfull \hbox generated by the tables with the greater vertical space (which is between text above the table and the table). Why does that happen? Is my suspicion right?
centerenvironment, use\centeringinstead. See When should we use \begin{center} instead of \centering?. – Peter Grill Sep 26 '14 at 16:17\centeringwould remove all the whitespace, while I'me perfectly happy with keeping part of it. The point is the tables with overfull\hboxes have more whitespace above them (but curiously not below them) than the last one which has no Overfull\hbox. And in any case in my specific case the suspicion has proven right, so the question is essentially theoretical, not practical. – MickG Sep 26 '14 at 16:21\trivlistwhich I failed to do once) to be «because ofcenter», but «Why is there more v.s. in some cases than others, where "some" seems to be the case of Overfulls incenter?». – MickG Sep 26 '14 at 16:28