Morphine and fentanyl aren't really that complex; ketamine is a wee bit more, but not that hard.
The differences between morphine and fentanyl aren't really that significant and probably don't mean much in the real world. Fentanyl is a bit more lipophillic so has a faster onset and shorter duration of action; but honestly, it's probably only about 30 seconds to one minute or so which isn't that big of a deal when you think about it. The "big" selling point for fentanyl is it releases less histamine so those who feel yuck with morphine have less of this effect with fentanyl but by-and-far the number of people who report feeling "yuck" with morphine to such a significant degree to justify giving them fentanyl is probably one in a zillion.
Fentanyl is about 10x more expensive than morphine so unless there's a very, very strong indication to give it, I don't see it as being overly necessary personally.
Ketamine is not an opioid analgesic but has some opiate receptor affinity so produces some analgesia but the main effect, IIRC, is to disconnect the sensory areas of the thalamus from the cerebral cortex by increasing release of GABA. This means the patient still may have pain but their brain is not aware of the pain. It is also advantage because it maintains airway and breathing.