With careful use of the \phantom
family of commands, you can get proper alignment inside and outside of the cases
(i.e., the second portion of your equation) as well:

This is a general solution that I often use and will work across different environment as well. We fix a size for portions of the equations, and use \makebox
to set that text in the specified fixed width. You can specify this fixed width as in:
\newcommand{\FixedSize}[1]{\makebox[1.5in][l]{\ensuremath{#1}}}%
This allows you to easily adjust this width to get the display that you want for the appropriate portions of the equation.
A better solution is to automatically compute the required width using the calc
package's \widthof
command. For this we select what is the widest portion that we need to be able to accomodate and then compute the width of that. You can do this all in one line, but for readability I have defined \WidestPart
separately, and used it to compute the width.
One slight complication in this specific situation is the left brace from the cases
. To adjust for this I defined \PhantomBrace
which produces a horizontal space equivalent to the width of the brace used for a three line cases, and include that in the adjustment of the first equation.
I added a \quad
to separate these two portions but any value can be used here.
\documentclass{article}
\usepackage{calc}
\usepackage{amsmath}
\newcommand{\WidestPart}{\ensuremath{aT\left(\frac{n}{b}\right) + n^{c},}}%
\newcommand{\FixedSize}[1]{\makebox[\widthof{\WidestPart}][l]{\ensuremath{#1}}}%
\newcommand{\PhantomBrace}{\hphantom{\left\{\vphantom{\begin{cases}\\\\\end{cases}}\right.}}%
\begin{document}
\begin{align*}
T_{in\ general}\left(n\right)&=\FixedSize{aT\left(\frac{n}{b}\right) + n^{c},}\PhantomBrace\qquad a\geq1, b\geq1, c>0\\
T_{cases}\left(n\right) &=
\begin{cases}
\FixedSize{\Theta\left(n^{\log_{b}a}\right)} \qquad a>b^{c}\\
\FixedSize{\Theta\left(n^{c}\log_{b}n\right)} \qquad a=b^{c}\\
\FixedSize{\Theta\left(n^{c}\right)} \qquad a<b^{c}
\end{cases}
\end{align*}
\end{document}