"Lasgun" is a contraction of "laser gun". Lasgun = laser gun, AKA Hand-held Directed Light Weapon. In the Dune Universe, the interactions between a HhDLW and a Full-Body Portable Force Field (shield) result in a catastrophic explosion.
Now, we know that all the people in a rung of the ladder know who made it to that rung, right? So obviously they would be able to research their potential opponents, and in a best-case scenario, prepare in such a way that no matter who they go up against, they have a chance of winning.
So Paul would likely know of Ezio's training, and vice versa. Same with equipment possibilities. What it all comes down to, in my opinion, is less of a matter of who is the better combatant and more of a matter of luck.
Assuming that Paul, Ezio, and the other competitors would have similar skill levels (remember, there has to be chance, however slight, for either party to win), it's not hard to deduce that either Ezio would win, Paul would win, or neither would. I think the third option is the most likely, given that Ezio and Paul both have mystical training and demi-deity power potential, as well as the various blades, armors, and ranged weaponry available to each of them.
It's logical to assume that Ezio would have a full complement of gear, that being Hidden Blades x2, Longsword, Short Blade, Throwing Knives, and maybe Altair's Armor to give him a fighting chance against Paul with his shield.
Paul would likely have a shield (which, to my knowledge, can be used to exclude things on the molecular level or not - it all depends on how the user calibrates the shield) as well as a bladed weapons (perhaps the crysknife?), a shield, and either a lasgun, dart gun, or both, third option being most likely as it gives him a fair chance of defeating anybody.
We also need to take into consideration the terrain. Both Paul and Ezio are unfamiliar with deep jungle; Ezio works mainly in cities while Paul kicks ass in the desert. However, they can both use the natural hiding places provided by the jungle to their respective advantage. The terrain also provides a disadvantage; trees and undergrowth block sight-lines while twigs and such are not conducive to stealth.
It really comes down to who would be able to get the drop on the other first. Ezio is a Master Assassin, while Paul is a Mentat and isn't exactly useless in a fight.
I do think Ezio would win, however, simply because he is more used to vertical movement as a means to gain the advantage of surprise over his opponent. Remember that Altair's Armor is black (thus helping him blend into shadows more easily), and if he did not have it, his robes would likely be dyed to take advantage of the terrain he will be fighting in - after all, the combatants do know that they will be fighting in and around a jungle on an isolated island.