I use Elixirs for both recording and performance. They are awesome strings. But, like any other string brand, they are bright and supple for the first hour or two of use then settle into a more rounded, but still very bright and manageable tone. The tone and intonation from the strings are consistent for a very a long time, which is what you want when recording. I have used other brands in the past whereby the tone of the strings have fallen off dramatically over just two days.
The strings on my J are D'Addario half wound and I use those strings for that bass only for sessions whereby I need a bit more classic thump in my tone which I can't get from fresh Elixirs. Plus, there's a little less string squeak with half wounds which some engineers love. Flats are good for a nice warm mid range and work really well for a classic tone. They will last for a very long time, but they will eventually lose their intonation over time.
It all depends what approach you take and which result you want. If you want a clean, flat and hi-fi tone...use fresh strings. If you want a more classic and rounded tone...older strings are fine, but half wound strings are becoming quite popular for recording these days. Give them a try. I don't like using old strings for hygiene reasons more than anything else.