A lot of it comes down to how many options I have for dice modification. For example if I'm using Screed I'll be much more aggressive with Ordnance Experts, because if two hits turns into hit/blank I can spend one and add a crit. So with him or something that says "spend a die to..." I'm a lot more likely to reroll a decent result and hope for a better one. I only reroll red dice if they come up blank (or excess accuracy results) because the odds of improving from one hit to two are pretty low.
If I'm shooting at anything that can scatter I'll reroll any dice that could show an accuracy symbol. All the double damage results in the world are useless if I don't block the scatter token. Scatter tokens aren't found on anything especially durable so even if I lose a lot of raw damage in the process I'm still going to be close to killing the target.