Pros and cons? They're pretty different, but it's hard to give a generic list of pros and cons.
Both are constant current buck regulators, which means they take some arbitrary input voltage and drop it to the appropriate voltage to maintain your desired current in the LED string. The CAT4101 is a linear regulator, which means it drops the voltage by converting extra power to heat. The PT4115 is a switching regulator, which means it uses a transistor (inside the IC) and an inductor to knock the power down. It's more efficient over a wider range of input

utput ratios, but since our setups are highly controlled, that sort of flexibility isn't very important (IMHO).
The other main differentiator between LED driver ICs is dimming methodology. Luckily, both the CAT4101 and PT4115 accept analog or digital signals over a pretty wide range of frequencies, and both can dim down to a very low duty cycle.
Linear regs typically have lower parts count and easier implementation but the chip you've found is extremely simple for a switching regulator.
If you can get them for 25 cents USD each, that's a very good price and will drop the "per LED" price by a pretty fair amount. That is, assuming they're easy to work with and don't have any huge issues once you get one built. Many pages ago we were all getting excited about the ZXLD1366 chip, which strikes me as somewhat similar to this chip, but it turned out to have some pretty horrendous issues and it didn't perform nearly as well as the datasheet claimed.
It definitely looks promising enough to spend a few bucks trying out. If I could get my hands on some I'd definitely experiment. What I'd do is set up a prototype board and try out different external components - order a few different values of inductor and sense resistor, for instance, and try them out to see what happens.
The chip has an input voltage range up to 30v, so I'd start by choosing a power supply. 24v supplies are commonly used and easy to get for cheap. Next you can choose an LED count, based on the power supply voltage minus the drop the IC needs (I don't recall seeing the drop in the datasheet). Then, pick the sense resistor, diode, and inductor based on the info in the datasheet.