could blaze the tires until I put a set of Dick Cepeks on it. They just stuck to the ground.
Tires can make a world of difference one way or the other. My Caddy is a 320HP car, which would vaporize the stock Goodyear rears at will from a standstill...I really had to pay attention not to stand on it too hard without traction control turned on because it was so easy to spin the tires, even on dry pavement. Then I put a set of Nitto NT555 tires on it, and it became difficult to even brake torque the thing on dry pavement in the summer. Once temps dropped below around 55*F, it became much easier...I was shocked at how well those cheap tires hooked up. Lifespan was dismal though...
Worn tires also tend to lose traction the more they wear. The BFG Comp T/As I was running on the Z28 because useless as tires once they got below about 40% tread. It was like the tire had two compounds in the tread, and at around 40% I got into a super hard compound, which meant little traction. Same thing as the Caddy...was almost undriveable because the rear end let loose so easily. So if the old truck always had old, cheap tires on it, and you now have newer, good tires on it..that could make a big difference.
But there are so many variables tied into whether a vehicle can easily spin tires or not...the old TBI 350 long block (basically stock TBI truck motor, with a RV cam, long tube headers, open exhaust, Weiand dual plane intake, and Edelbrock 1406 carb) that was in my K5 prior was a fairly strong motor too, but wouldn't break the 33s loose even with a 700R4 & 3.73 gears. On the other hand, the 489 in there now has zero issue roasting those same 33s with a 4L80 2.48 1st gear by just rolling into the throttle. You're only talking roughly a 20% difference between 1st gear ratios between a TH350 and TH700R4 trans. Not insignificant, but replacing a 350 with a 700 isn't going to instantly change a slug of a truck into a tire vaporizing machine either.
As others said, if you've got full time 4WD in the truck, you're not likely to get those tires spinning with anything short of a lot of additional HP. Even with part time 4WD, going from something like a 3.73 gear to a 3.08 gear is likely going to cause it to MUCH more difficult to get tires spinning. If you went from low grade, small diameter street tires to a larger off road tire, that too will make a big difference. That was the case on my old Jeeps...went from the stock 28" street tires that were easy to spin with a brake torque with the stock 4.0L I6 and 3.73 gears, to 33" mud tires turned those things into a slug that was barely capable of chirping the tires. Changing out the gearing to something like 4.56 or 4.88 was needed to bring the the perceived power loss back.