Depending on your actual diagram you want to use the TikZ library positioning loaded by
\usetikzlibrary{positioning}
and the base right=of <other node> key.
Either way, you want to use the text height key. You also want to set the text depth key for the very same reasons if you have text of different depth (in your case, the \mu is lower/deeper than the subscript 0 in both nodes).
If you expect only general characters like A-Za-z0-9 and simple subscripts you can easily use font=\vphantom{Ag} which is similar to font=\strut but doesn’t add that much height and depth (which you don’t notice as you use minimum size=1cm here).
The difference is that the keys text height and text depth do set the height and depth no matter the content while \vphantom and \strut only set a minimum height/depth (so to speak).
Code
\documentclass[tikz]{standalone}
\tikzset{gate2/.style={circle, inner sep=+0pt, fill=white, draw=black, minimum size=+1cm}}
\newcommand*{\tfbox}[1]{{\fboxsep-\fboxrule\fbox{#1}}}
\begin{document}
\begin{tikzpicture}[gate2/.append style={anchor=base}]
\node[gate2] (mu_0) {\tfbox{$\mu_0$}};
\node[gate2] (Lambda_0) at (2, 0) {\tfbox{$\Lambda_0$}};
\draw (mu_0.center) -- (Lambda_0.center) (mu_0.base) -- (Lambda_0.base);
\end{tikzpicture}
\begin{tikzpicture}[gate2/.append style={text height=\heightof{$\Lambda$},text depth=\depthof{g}}]
\node[gate2] (mu_0) {$\mu_0$};
\node[gate2] (Lambda_0) at (2, 0) {$\Lambda_0$};
\draw (mu_0.center) -- (Lambda_0.center) (mu_0.base) -- (Lambda_0.base);
\end{tikzpicture}
\begin{tikzpicture}[gate2/.append style={font=\vphantom{Ag}}]
\node[gate2] (mu_0) {$\mu_0$};
\node[gate2] (Lambda_0) at (2, 0) {$\Lambda_0$};
\draw (mu_0.center) -- (Lambda_0.center) (mu_0.base) -- (Lambda_0.base);
\end{tikzpicture}
\end{document}
Output

anchor=baseto thegate2style. The default anchor is thecenteranchor. If you load thepositioninglibrary you can dobase right=of mu_0at the second node. The value ofnode distanceis then used as the distance between the nodes. (Unrelated to your actual question: Should\tikzsetor\tikzstylebe used to define TikZ styles?) – Qrrbrbirlbel Sep 13 '13 at 21:07anchor=basemoves the shapes, unfortunately: the circle containing mu becomes lower than the Lambda circle. – vuvuzela Sep 13 '13 at 21:16\usepackage{positioning}leads to errorLaTeX Error: Filepositioning.sty' not found. [\usepackage]` – vuvuzela Sep 13 '13 at 21:18\mu_0is not as high as\Lambda_0as TikZ positions the boxes containing the text in the center of the shape. You will need to work with\vphantom{\Lambda}in the\munode or usetext heightand sometime eventext depth. —positioningis a TikZ library not a LaTeX package, so you need to do\usetikzlibrary{positioning}, the problem is still the same though. – Qrrbrbirlbel Sep 13 '13 at 21:32