Now as long as they provide a tracking number(AWB) or the like you can see the progress with, then that does help greatly. If you can even have GPS tracking the last part and notification when hour away or within 5 minutes, well that would be great.
So that is why I don't get too excited about same day shipping. It is the hubs inbetween and there cut-off times that divide up the day so you could ship at 11pm and miss the 10pm cutoff for the hub transit and have to wait until the next one at 10am. In that case for you it makes no difference if 11pm or 9am. Though anybody who has had tracking information will know how weird some routes can be and wonder why they sit for almost half a day at some locations. Then there are customs if different countries are involved and more fun.
For me better item tracking would win over same day dispatch. I'd take a 5 day delivery window over a 1 day one if it meant I could refine the delivery time to a hour and not AM/PM. Though that may just be me.