Hi!
It's true that tantalums are stabler and don't age like electrolytics. I don't think they have any effect on noise in the signal path. They have lower ESR than electrolytics, which means they look like a lower resistance to the rest of the circuit, and which in a given case might work better. The "sound" of tantalums is controversial. Audiophiles tend to hate them, although they are used in the signal path of the most coveted Neve gear. It's a fact that tantalums don't like to be reverse-biased, which is what happens if they are used a coupling caps in a bipolar-powered circuit, because this causes crossover distortion. However, in a single-supply circuit (like a stompbox) where there is a DC bias on the coupling cap, there's no problem of crossover distortion. The only big downside of tantalums is, they cost about ten times more than the equivalent electrolytic, and the price of tantalum happens to be going up because of limited supply of the mineral.
Joe