I don't see an issue with growing the two together as seedlings and then transplanting them into their own setup.

No way the taste of either could be affected due to proximity. But sweet peppers are generally growing faster and bigger, and if producing big pods (like bell pepper types), they basically require higher nutrient strength and even higher Nitrogen ratios.

I'd chose some varieties that are compatible (not completely different) by plant- and pod size. In that case you can grow them to maturity in the same system. Otherwise you still can try it, but you'll need to compromise with nutrient strength. Let's say 1.5 versus 2.0 mS/cm (EC)

I agree with lucas. The taste won't be affected. I'm trying the same experiment in a home made flood and drain system. I have half hot peppers and half sweet peppers(10 varieties total). They're about a month in and besides the prior bug problem, the plants seem to grow well together, so far. They're growing peppers and aren't showing any deficiencies. I'm running the nutrients at a medium level around 1.5 EC.

Thanks