Casals also said that there is a difference between C# and Db.
He said this in an interesting book, which I have sadly lost, Conversations With Casals.
Actually, there's a difference with all notes, even unaltered ones, depending on which tonality you're playing at the moment, if you want the chords between all the players to sound in tune and full, so that the tensions between modulations have the impact that they require. Specially if you play in an ensemble with instruments without fixed intonation, like an orchestra, you'll quickly learn that all the notes have to be arranged depending on which chord you're in at the precise moment!
Curiously enough, bass players have the tendency to play sharps well, a bit sharp; and flats well, a bit flat. I don't know why that is, but the moment you start relating this notes to the most common tonalities in orchestral music, you get into really big problems. Sharps are usually too high and flats too low so that tonalities lose their character, their colours get shaved off and modulations don't sound as imposing.
I'll take your C# and Db to illustrate the relation of altered notes IN HARMONY (and how their sharpness/flatness relates to when they are the fundamental/tonic of the tonality and therefore 'absolutely' in tune): C# is the third of A major, so it has to be flat to sound in tune. But if you're in F# (mind you, major or minor) that C# is the fifth and has now to be completely in tune/a little bit high, even if just a tad. About that Db: if it's the third of a Bb minor chord it has to be a bit high but if it appears int he music as the 7th of Eb it has to be a bit flat.
A note that is specially problematic with basses, IME, is the Ab on the E string. Because it is more difficult to reach than other notes on that position and it requires a bit more strength to be pressed, it happens quite a lot that it is very flat. This a big problem if you're in Ab (minor/major) because it is actually a very bright note in most chords in orchestral (quite natural to most brass instruments), so that when the basses are too flat no one knows where to play their notes anymore.
I hope I could explain my point well enough!! This applies mostly to orchestral music, mind you!!
To wrap up, this is the thing, for me at least: there are a couple of rules for each note that I always follow while playing in orchestra. Like, most C#'s, G#'s, F#'s will be flat (because they are most commonly major thirds and 7ths); most Eb's, Ab's, Bb's will be high/perfect (mostly they appear in classical music as fundamentals, 5ths or minor 3rds); and that with each note. They get tweaked in the moment depending on whats happening around, not only the tonality and function of a note at a particular point in the piece, but also of the colleagues that are playing with me (as you might know, strings usually go flat during performance and winds go up).
It's a nice thing to keep one's mind sharp at all times and quite helps get through long performances, but that might be just me!!
