Control spacing around table caption

The spacing is caused by the caption package, which is loaded by subfig. You can adjust the two parameters aboveskip and belowskip provided by caption using something like \captionsetup{belowskip=12pt,aboveskip=4pt} in your preamble. Note that below and above have the meaning as it would make sense for figure captions below a figure: aboveskip is the space between the content and the caption (which would be above the caption for a figure caption that's set underneath the figure, but below it for a table caption that's set above the table), belowskip is the space between the caption and the surrounding text.

Here's your example with the aboveskip and belowskip adjusted:

\documentclass[a4paper, 12pt]{article}
\usepackage[T1]{fontenc}
\usepackage{subfig}

\captionsetup{belowskip=12pt,aboveskip=4pt}
\begin{document}

\begin{table}

\caption{Internal exon scores}\label{tab:internal}
\begin{tabular}{|c|l|l|}
\hline
Ranking&Exon Coverage&Splice Site Support\\
\hline
E1&Complete coverage by a single transcript&Both splice sites\\
E2&Complete coverage by more than a single transcript&Both splice sites\\
E3&Partial coverage&Both splice sites\\
E4&Partial coverage&One splice site\\
E5&Complete or partial coverage&No splice sites\\
E6&No coverage&No splice sites\\
\hline
\end{tabular}

\caption{External exon scores}\label{tab:external}
\begin{tabular}{|c|l|l|}
\hline
Ranking&Exon Coverage&Internal Splice Site Coverage\\
\hline
X1&Complete coverage by one or more transcripts&Splice site covered\\
X2&Exon coverage >= 80\%&Splice site covered\\
X3&Exon coverage < 80\%&Splice site covered\\
X4&Exon coverage < 80\%&Splice site not covered\\
X5&No coverage&Splice site not covered\\
\hline
\end{tabular}

\end{table}
\end{document}

Since you use subfig, you can adjust this by \captionsetup of the caption package, for example:

\captionsetup[table]{aboveskip=0pt}
\captionsetup[table]{belowskip=10pt}

With these adjustments, you will get this output:

without loading another package use

\usepackage{subfig}

\let\belowcaptionskip\abovecaptionskip