Bold math: Automatic choice between \mathbf and \boldsymbol for Latin and Greek symbols?

You can use both commands together and define something like

\usepackage{bm}
\newcommand{\vect}[1]{\boldsymbol{\mathbf{#1}}}

which should work for most cases.

The macro

\newcommand{\vect}[1]{\boldsymbol{\mathbf{#1}}}

does not work with mathtime pro lite fonts (and from the comments it appears that it does not work with mathpazo either). Another approach is to simply check if the argument is A-Za-z.

\usepackage{bm,xstring}

\def\VEC#1%
    {\IfSubStr{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}{#1}
        {\mathbf{#1}}
        {\bm{#1}}}

This is inefficient since it performs the substring check for each execution. One could define macros \VEC@A, \VEC@B etc (using a simple loop), and then check do

\def\VEC#1%
    {\ifcsname VEC@#1\endcsname
        \mathbf{#1}%
     \else
         \bm{#1}%
     \fi}

Although this doesn't answer your question, have you tried using the bm package? Then $\bm{\omega}$ gives a bold omega, $\bm{u}$ gives a bold (math italic) u, and $\bm{\mathrm{u}}$ a bold roman u.