Booke23,
The 172 probably has a better short field perfomance than the PA28-181.
As to load carrying it depends upon which mark of 172/PA28 you're talking about. From my experience the 172P and the old slab winged PA28-181 Archer 1 were about the same, earlier marks of 172 had a bit less useful load. I'd say that the Archer 1 was only 5kts faster than the 'old' 172s I flew. The new 172s (172R and 172S) cruise at about 110kts, and are very nice.
The 172S has a 180hp engine, so matches the Archer on power, and has the advantage of being fuel-injected. For the life of me I can't understad why Piper didn't put fuel-injected engines into the Warrior III and Archer III.
Brooklands