In either case, each left pretty extensive records, especially of his military adventures. Remember also, the Egyptians recorded literally everything, including the sales of slaves. Hundreds of such sales records exist from this period, but none mention anything to do with Hebrew slaves. Indeed, the entire historic record is mute on this point.
Sorry I took so long in replying, but your post deserved a thoughtful rsponse. Your links to the two Pharoahs contained some interesting information, but your timeline may be in question.
First, from the source you directed me to, Wikipedia, there is this interesting tidbit:
http://en.wikipedia.org/wiki/Merneptah
As you can see, the 3rd paragraph refers to the "only" mention of Israel from Ancient Egypt, on the:
http://en.wikipedia.org/wiki/Merneptah_Stele
Now, some of my sources offer completely different timelines, such as this "traditional" Exodus at 1250 BCE:
http://www.spiritrestoration.org/Church/Research%20History%20and%20Great%20Links/timleine_of_the_old_testament_chart.htm
This earlier, circa 1450 BCE Exodus (close to your timeline):
http://www.mustardseed.net/timeline/timeline3.html
And yet another placing the Exodus at 1496 BCE:
http://www.matthewmcgee.org/ottimlin.html
Now, please don't take this as me attempting to impugn your knowledge on Ancient Egypt, Lord knows, I am not as expert myself. But the known recordkeeping in Ancient Egypt looks to be quite uneven, especially during the Hyksos period (2nd Intermediate). Coincidentality, that time period coincides with most of the 400 years mentioned as the time of slavery in Egypt.
In short, my opinion is that you may have overstated your case for Ancient Egyptian recordkeeping. I would be particularly interested in the source of the slave sales records you cited. Junior, I'm not trying to play "gotcha"; I want to learn!
And before you tee off on the differences in the timelines, let me just offer that the study of the History of the Bible, once you get past Chapter 8 of Genesis, is a serious discipline with its own schools of thought, disagreements, and intra scholar controversies. Roughly akin to some of the disputes among the "gradualistic" and the "upheaval" schools of thought on macro - evolution.
There are still a lot more places to dig and a lot more things to discover about antiquity.