I both agree and disagree with Billm and JC.
Though a 5E3 (the Tweed circuit with which I have the most experience) can be forgiving when turned up into OD territory, I find mine to be very revealing when playing my equally unforgiving esquire/parts-squire. The neck of the guitar has rather beefy frets, and if I grip the strings too hard when playing chords, thus bending the strings down to the fret board, the height of the frets make the strings bend out of tune.
The 5E3 certainly doesn't let that pass unnoticed.
Especially not when recording. It is a sobering experience for sure, guess I'll have to practise some more.
So I've noticed there is definitely a difference between playing a fat string bass with tiny frets - my main instrument - and playing a guitar with comparatively puny 0,11 strings and beefy frets...
My experience is that this only applies for chording. When playing more solo:ish bluesy stuff there is so much bending going on that you use your ears to determine the right pitch rather than the frets.
Now I hope this doesn't put me in the "more snobby guys here, so be careful" cathegory. Forgive me JC!
On the other hand, I cannot think of a more unforgiving amp than the 5E3 when it comes to getting a wonderful tone. Give any monkey at your local zoo a tele, an instrument cable and a 5E3 and I bet my bottom dollar he'd be able squeeze some sweet tones out of the stuff at his very first try!