I currently keep BTAs and Giganteas in my tank and haven't (YET) had a problem with this setup. Everyone stays where they are, unless I mess with the flow or the lighting. However, I try to take every precaution I can to keep the water clear. I run carbon and skim extremely wet (I fill my large skimmer cup in merely three to four days). This doesn't mean I recommend mixing anemones though. Just because I don't have a problem now doesn't mean I won't have one later.
I should also note that I had two previous BTAs that did not appear to enjoy sharing the tank with other anemones, even BTAs. In Japan, we have several types of anemones that seem to use the BTA label in English (Entacmaea ramsayi, maxima, sp. M, quadricolor, actinostoloides). Hard to tell them apart, but I haven't had luck mixing the types. All my BTAs currently are all actinostoloides (red) now and possibly had the same parent. These coexist fine with the giganteas. (FOR NOW)
I had an LTA briefly, and while that coexisted fine with BTAs, it did not coexist well with the carpets. I don't think I will be trying that again. In any case, I think chemical warfare is harder to avoid as the tank gets smaller. In my previous 50 gallon, mixing anemones got me much more disastrous results than in my current 130 gallon.