Are they as effective as nukes?
Bioweapons can be a nightmare. End of world potential. Extremely cost effective system. Problem with them, until fairly recently, is that the more effective they are, the more danger they present to the user. This has become somewhat less of an issue with genetic engineeing.
Chemical weapons are more scary than truly effective as actual "weapons" A couple tons of CW weapons (including weapon casings) will kill/injure part of a major city. A couple tons of modern nuclear weapons will wipe out at least a couple cities (a B-61 gravity bomb weighs 700 pounds and has a yield of of to 340kT, a W88 missile warhead, yield 475kT weighs ~800 pounds).
To the OP question: A span of 10-30 years between wars is reasonable, depending on how alliances shake out. For example, after WW II NATO and the Warsaw Pact would have been ready to go at it hammer and tongs by 1955, only ten years after WW II, but they had been allied in the previous conflict and, at least in the case of the West, had been able to recover remarkably quickly while the Soviets had managed, rather miraculously, to rebuild military capability during a massively destructive war. After a major engagement in 1955 there would have been at least a decade, more likely two to rebuild and refill the various treasuries.
So a quick and dirty estimate would be 1955,-1958, 1973-76, 1996-2000 (very possibly with a different set of players, potentially the PRC vs. the West over what is left of the USSR or the Soviets and Chinese deciding the future of Eurasia) with two power block gearing up for the next war right around now.