Morning all,
Goku999 is right, there's no
ideal height for badminton (that is, excessive height provides no inherent advantage as in other sports such as basketball, where the aim is to throw a ball into a target 10 feet in the air). This is part of the appeal of badminton (almost anybody can play it, if not well

). However, the simple presence of the net does give a
lower limit to the feasible height of a player (anyone under around 5' 3'' will have trouble striking downwards close to the net).
As to the pros/cons of tall vs. short: as Goku999 said, being tall gives beter angle for overhead shorts (and a longer reach as well) but makes retrieving the bird from near the floor more difficult. Also, the taller players seem to have more difficulty dealing with net-height drives (especially towards the non-racket shoulder). The shorter players receive these shots at a more comfortable head-height and so can respond better.
Having said all this, one of my regular doubles partners is 14 years old and about 4ft 9in (his head comes up to my armpit

) and he is probably the most agile net player I've ever seen, as he's on the floor diving about 80% of the time. More importantly, his
mind is perfectly attuned to badminton, so he knows
where to place a shot even if he doesn't quite get it there every single time. Just shows what good mentality can allow you to overcome...