Pleas stop, I actually HAVE a modern day laser printer and had an inkjet printer (pretty nice one too). The laser printer starts up way faster and can print its first page at a fraction of the time that my inkjet would have its first page printed. And that was from a cold start, zero power. If it started from sleep mode, it would be even faster. My inkjet would freakin' cycle through some stupid pointless sequence for what seemed to be forever. I'm assuming it was running a system check, possibly cleaning heads. And THEN finally, something would print. Freakin' annoying. This was typical behavior of some of the nicer Canon/Epson inkjet printers.
Again, first page out, HP laser printer winner, no contest. You have to be running some crap inkjet printer that isn't checking alignment, and doing a general system check at start up in order to have its first page print "immediately." There is no "immediately" with inkjet printers, at least not on nice ones.
I actually have a modern day laser printer AND a modern day inkjet. The technology behind the laser printer involves the use of a heating element called a fuser and that item requires time to warm up.
If both printers are powered up from cold the inkjet will likely go through an initialization sequence that can take about a minute. This sequence involves head homing and in many cases some ink flow to check/clean the heads. If, however, you leave the printer on it will accept a new print job and begin printing almost immediately.
Laser printers do not have the same initialization sequence but does require the fuser to be warmed up. Different lasers require more or less time to power up the fuser just as different inkjets require more or less time for its initialization sequence.
After both have been powered up and its been some time since the last print job they will go into a sleep/idle mode. Then, when the next print job is sent they have to come out of sleep and prepare to print. For an inkjet that is pretty much limited to pulling in the first sheet of paper and beginning to print. With a laser, however, it must warm up the fuser that had been turned off in sleep/idle.
So, if both are started from cold the time to print the first page is likely to be about the same with some lasers being faster than some inkjets while some inkjets are faster than other lasers. I'll call that a draw.
Once they've been powered up and a print job is sent with both printers in sleep/idle the inkjet is almost always going to be faster to print the first page.
Brian