I use two basses anyway, one tuned to E and the other tuned to Eb. We have about five songs that are in the latter tuning in our set so we play them one after the other, and then change instruments to return to standard tuning. Whichever bass I'm not using at any given point becomes a de facto spare. They're both Player Series Precisions with the same pickup, wiring loom and strings, so they sound pretty similar to my ears, and as mentioned above by @neepheid, no punters have ever mentioned any difference in sound regardless of which I use.