What are the major drivers of cost/price differences between Cessna 172 and Piper Cherokee?
There are a lot of factors here but in reality a 172 and a Cherokee are about the same price, lets look the reality.
First off a huge chunk of people rent instead of buy. In this regard at the two airports I have been flying out of have both the 172s and Cherokees (both of which I have rented) are the just about the same exact price (all prices in USD).

Cherokee Wet  : 108
VFR Only 172: 103
IFR 172 : 113

The used prices (how a lot of people buy planes like this) span the field and I would say are on par (as per my latest perusing of Trade-A-Plane). That being said you can get a beat up Cherokee 140 for in and around 20K and a beat up 172 for about the same price (at least from what I have seen listed). At the same time you can get a fully loaded Cherokee 180 or 235 if you go complex with dual GPS/COMS and other toys for the better part of 60-70K, same for the 172s.
Yes they are similar planes but the truth is that the price things actually trade hands for is often not disclosed and is almost always not the list price in terms of used stuff. There is a bit of preference as well, if you trained in a Piper you may be more inclined to stay in a Piper and likewise with the Cessnas.
As for safety, the 172 is a very safe plane by anyone's standards. Then again so is the Cherokee and it seems that the argument can go on forever but the numbers are the numbers (accidents per 100,000 hours of flight)

The 172: 6.17 overall accident rate.
The Cherokee: Cherokees came in at 6.86

In reality a small difference, but lets be honest they are about on par. For what its worth, the Cherokee numbers include the Arrow which is a retractable and suffers from the proverbial gear up landing as well as other things that make a retractable potentially fail more than a fixed gear plane. This may account for the difference in safety record (again, a very slight difference).
While similar on paper there are some mission profiles that allow the planes to serve different roles and may make the 172 more attractive in some cases. The high wing design allows for excellent downward view which makes the 172 a great plane for aerial surveying/photography/pipeline check ups and similar tasks. The 172 also sports two doors compared to the single one on the Cherokee. That being said some feel as though the 172 is a bit easier to get into for the less nimble, but I am young and nimble so I can't speak to this. There are also those who like the high wing design for landing on grass or other back country flying due to the increased ground clearance of the wing allowing you to avoid obstacles.

From an aircraft family standpoint the Cherokee 235 had a much better useful load than the highest power 172's. However even the 180 Cherokee has a better useful load than the 180 Cessna. When you are flying around a family this is worth considering.
Although Cessna had it to an extent, Piper has always had the selling point of &quot;stepping up through the planes&quot;. The idea being that your mission (as time went on) would be to go faster, further, and higher. Subsequently you would need a bigger plane. They facilitated this by delivering a very constant platform in the, Cherokee, Arrow, Cherokee 6/Lance/Saratoga then up through twins with the Seminole and Seneca if you need to go there. While I'm not sure I have ever seen any real data on this, I do have a real world experience with a buddy of mine who has been flying for about 25 years.
In response to the question &quot;Have you ever owned any other planes?&quot;

Yeah, I had an Archer for a while, it was a great plane. But then I had a third kid so I bought a Saratoga.

Like it or not the Piper sales model there worked.
You could also forgo common sense and just buy a Mooney because everyone else put the tail on wrong.