There can be many advantages depending on the ratings of the stock resistor. Based on the mistakes of the circuit designer, one can gain a lot from changing the capacitor. Since you can’t change the value of the capacitor, what one can change is the voltage rating of the capacitor. Higher the voltage rating of the capacitor, the more voltage it can produce at the output efficiently without any issues. The second thing that be improved is the tolerance of the capacitor, you’ll have to buy a bit more expensive capacitor but it’ll give you a better result for sure.
This is false in regards to voltage rating. The voltage rating is what the capacitor can handle. Let's assume a transformer secondary = 32VAC We simply multiply this by the square root of 2 (approx. 1.4142) Therefore, Working Voltage WV = 32VAC X 1.4142 = 45.25V. Thus, you want to use the next higher rating, which is 50v rating.
Now, when looking for a quality capacitor, you typically want the lowest ESR, along with the highest ripple rating that you can get within your size dimension. Capacitor uf values differ in their applications, but for a power supply section, the more the better. Cost has really dropped the past decade, so diminishing returns isn't such a big issue anymore.
Tolerance is primarily when you're dealing with sensitive applications like precise filters and crossovers. However, film caps are typically much better than electrolytics if you have the physical space and funds for them.
Cheers,
Brunk