Not a big fan of Dhrupad but I think thats because only the Mishra brothers really practice it. The structure of a general Khyal is a beginning portion of elaboration of the notes of the raga to be performed afterwards, without rhythmic accompaniment, generally in the form of what is called Aakaar (expressing notes using only the Aa vowel sound). This is followed by the lyrical portion of the raga, the bandish, the lyrics basically. Each syllable being deliberately chosen to correspond with an underlying note, in hindustani music generally written in the dialect of hindi/urdu called braj or brij basha. A fairly archaic language still spoken in a few villages in India.
The main portion begins usually in a slow portion, the vilambit portion, a lot of performers stay here for a good long time, giving Khyal its droning quality. This is followed by the medium rhythm portion, madhya lay, eventually ending in the fast drut lay.
Some great Khyal practicioners are Ustad Amir Khan, Ustad Rashid Khan, Pandit Bhimsen Joshi, Ustad Salamat Ali Khan, Pandit Jasraj (he can be a bit needlessly flashy), Bade ghulam Ali Khan (has a lot of more popular stuff, few recordings of serious music) and I suppose Ajay Chakraborty, Kaushiki`s father.
Instrumetal Khyal is broadly similar to the vocal style, but the use of instruments allows some aesthetic differences, the ability to elaborate some phrases that vocals cant. Overall the human voice can approximate more sound than any instrument, so it is favoured. I prefer the Sarod and Sitar.
During a Khyal performance the main vocalist is accompanied by a secondary instrument. This used to be mostly the sarangi, a grossly violin like instrument, but nowadays is increasingly the indian harmonium. A background drone in some notes of the raga is played by one or two tanpuras, large sitar like instruments which are played only by tuning them to the required raga and playing each string in succession repeatedly.