I enjoy that Delius piece - however I've never understood the general sentiment surrounding the Cuckoo - nasty, rapacious birds (from a human perspective).
Regarding the Rautavaara Cantus Arcticus - another piece I enjoy - it is what it is, being composed in 1972 and using the technologies then available (tape recordings). The composer therefore specifies that at certain points in the music, recordings of birds (that he made himself) are played on cue. He actually supplied a choice of two recordings, of the versions I've heard Lintu, Segerstam and Vanska all use the same one (which according to Vanska's sleevenotes is the 'revised' recording) and Pekkanen uses a different recording (also credited to the composer) with a more 'interesting' variety of birdcalls. Both versions are good of course.
Had he composed it 15 or more years later he might have used sampling tachnology, with the birdsong played in during the performance by one or more musicians - for example using keyboards, with a birdcall allocated to each key. I'd like to hear Cantus Arcticus done this way, it would allow a more natural randomness to the performance, and more flexibily of tempo for the conductor.