I've got most of my time in various Pipers, but I also have prob. 200 hours of Cessna time with close to 100 hours in C172 R or S models. I did my private training and most commercial work in a Warrior III, with my instrument work and commercial checkride in an Arrow III.....then I went and did my CFI initial in a C-172RG and my CFII in a 172M.
Both airplanes have their attributes for training. The whole Cherokee family is about as forgiving as an airplane can be in flight; the stalls are benign, there is little to no tendency to drop a wing even with positive spin inputs, and the stabiliator gives a very positive feel in pitch (this gives people transitioning from Cessnas fits). Pipers also have manual flaps at 10, 25, 40 and that magical "fourth" flap setting (pulling on the flap handle to get approx 45 degrees), and I much prefer that to the Cessna electric-slot style flaps and much prefer it to the "one one thousand" hold-down style flaps on older Cessnas.
On the other hand, you could never use the rudder pedals in a Cherokee and get away with everything including crosswind landings up to 7kts. In any model Cessna, you HAVE to use the rudder or you can feel the airplane slip all around a turn, and as a CFI I appreciate that. I get so aggravated when I get students from other instructors that never emphasised use of the rudder in the Pipers. You can usually tell these pilots because they don't know how to land in a crosswind or operate on the runway centerline. Also the Cessna spring steel landing gear is much more forgiving to student pilot landings than the Cherokee's air-oleo strut. I've felt some landings where I thought the gear went through the top of the wing. Another thing I like about Cessnas is the convenience of two doors, and the ability to open the windows on a hot summer day, even in flight - this cannot be understated! A Cherokee is like an oven in the summer.
Albie was right about floating...for every knot above book approach speed you are (assuming calm winds), you can expect to float AT LEAST 75 feet. When I do accuracy landings in a Warrior, I fly it at around 55kts (book approach speed 63, Vso 44) to prevent excess float, and you can get plenty anyways out of ground effect at that airspeed. Its a sinch to hold that thing off...
As far as instrument training or flying goes, the Piper will whip the Cessna all day long. I dunno about the old hershey bar wings, but the Warrior wing on any of the newer Pipers is as stable as you can get. The Pipers are slower and burn more gas than comparable Cessnas. This could be a factor for taking longer trips, but if you gave me a choice between an Archer and an SP to fly a long IFR trip, I'd take the Archer and get there a few minutes later.
I enjoy flying Cessnas, and had a blast flying a 150 from GFK to LAF in May 03 coming back from SAFECON at the University of North Dakota at 1500agl. A Cessna is a great plane for sightseeing, pictures, speed or crosswind landings. A Cherokee, in my opinion, is a vastly superior instrument platform, more comfortable and is a better trainer because of how forgiving it is to mistakes.
As far as your training goes, it sounds like you have used the King CDs in the CPC program, I think Jepps are probably similar. If its a Part 141 school, most things should be familiar to you.
Best of luck in your training, and I hope you like the -181. By the way, if it has air conditioning, your useful load isn't jack
