There are a couple of differences - putting in a spinal and having it work takes time (10 mins or so), which in a real emergency you may not have. So some emergency CS are under general anaesthetic. If you already have an epidural in from the labour then they will try to use that for the CS as well.
The other difference is that you don't get to choose who performs your emergency CS - you get the obstetric registrar or whatever obstetrician is closest!
If your bub is in distress then the paediatrician gets priority access, regardless of whether it is emergency or planned.
The get-the-baby-out part of an elective CS is over very quickly anyway (my forms list "labor" as 3 mins from cut to placenta out...). Stitching you back together and cleaning up takes some time - which if bub is OK and you are awake you will be able to spend getting to know bub.