bleh. Those are very nebulous questions.
Tires basically balance treadlife, comfort, dry traction, wet traction, snow traction, ice traction, and price. Each individual tire will have different strengths and weaknesses in each area. Specifically, Dry traction comes at the expense of nearly every other category to some extent. Also, within the term "traction" implies a lot of different things from steering response to lateral grip to bound and rebound damping. Even at this level, we're making gross simplifications.
Speed ratings, load ratings, and temperature ratings also have an effect on a tire. Some tires make compromises in some of the areas listed above in order to achieve a given weight, speed, or temperature rating. These factors are sometimes secondary, but sometimes not. For example, extremely low profile tires may compromise nearly everything in order to simply be rated for the weight they will need to handle with so little sidewall. A more general example of this though is the stiffer sidewall needed for higher speed ratings. Generally, there is a big gap between V and above rated tires and things below in terms of sidewall stiffness. Stiffer sidewalls are made of more expensive designs so price, and performance, can vary even within two tires of the same size and design just with two different speed ratings.
An additional complexity is that you've picked one traditional tire and one RFT tire. RFT is run-flat. Generally, run flats are a concoction designed for safety that did not pan out. It puts huge burdens on tire design which lead to high cost and shit tires. Just ignore anything with RFT, realizing that RFT itself is a big reason for some of the cost involved in those particular tires. If nothing else, it's a markup for the select few cars that expect RFT tires. Limited market means higher prices for the specific size tires they need.
As far as the DW vs the RE050, they are both the same type of tire. Pricing, which seems to be of central interest to you is complex and not linked exclusively to attributes of the tires. Bridgestone is a well known brand and on some tires commands a premium just due to it's name. Also, some tires are older designs or newer designs and the wholesale cost will vary based on how much of the design budget for the tire is included in the price. Older tires are often cheaper because they have already made up development costs and are now priced closer to the cost to create individually.
And none of that gets into "which tire handles better?", which is a completely different question.
2015 STi: Still Stock
04 STi, 04 WRX: SOLD