Marty,
Yes, the short answer is yes a turbo diesel will pull better up hill, for overtaking at normal road speed and for pulling away under load.
Simply explained techcnical reason - petrol engines develop their power and all important torque at much higher revs, a diesels torque is invariably higher for a given size of engine and comes in at low revs, as low as 1800rpm in some cases which makes them ideal for that "slogging grunt" that is so useful for load pulling.
The new Santa Fe has a 2.2 CRD engine and has been higly praised in the press but even the old model with the 2.0 diesel engine would perform a deal better than your 2.0 petrol Trajet.
To give you a working example I used to tow with a 200 plus BHP V6 petrol Shogun - it was an ace towcar but screamed it's head off on hills and even changed down on motorway inclines when towing. OK the pace was still there but with the engine revving to about 4000 rpm to maintain 60 mph on an inclne it was not ideal.
Everyone told me that for a Big van the Isuzu Trooper 3.1 diesel was the one to have and so I swapped. Oh boy the difference was amazing - although it only has 110 BHP the torque is mountainous and comes in below 2000 rpm, the thing has so much grunt you could use it to pull tree stumps out.
Now with a van at 60mph you see a cool 2200 RPM and nothing much slows progress - on a long steep incline speed may drop to 55 but flick it out of overdrive and up it goes again to 60.