Hear hear! The local place didn't stock Pana or Yageo, nor Xicon/Lelon, but whatever floats your boat. What you can do if you are really picky is to match the original's footprint ( duh! - or at least lead spacing) but go higher in terms of voltage it can tolerate and temperature range, let your wallet decide.
So, for starters lets assume we have old-school brand X, 220uF, 25V, 5mm lead spacing (RM), 16mm dia. Today's caps can hold more energy in a smaller volume so we could find a replacement like a hypotethical Panasonic, 220uF, 63V, 5mm RM, 10mm dia, 105°C and less height. All good? Look at the max ripple voltage if you can find it (bigger is better) and the ESR (less is better). Parametric search (Digikey works for me) is your friend here. Yields this. Lifetime 10000hrs@105°C. Much longer at room temp... You'll find that general purpose caps start to drop off and specialist brands dominate the more you tighten your search params, this can be a quality indicator, but will take a larger bite out of your wallet.
Take the article name and search if you want to shop around.
Best of luck!
J