Evan and Scot each have multiple hats that you might see in pictures with the main difference being material and brim size. The choice in hat worn is dictated by weather and activity, with smaller brim hats being the choice for wear with taller packs and in and out of vehicles and larger brims for more protection in worse weather.
In general, they wear Sunbody Palm Leaf’s in the summer. The Sunbody hats have the best sweat band they have found. Unfortunately, Sunbody only offers fully vented with larger brims so for smaller brims, to wear with packs and in vehicles, they have eyelets installed around the perimeter of the crown. See the photo and information above. That venting allows any breeze to blow through to keep them cool but does not detract from sun protection.
During the more inclement seasons both Evan and Scot wear fur/felt hats. If you are unfamiliar with those types of hats, they range from 100% felt to 100% fur (typically beaver, but sometimes buffalo) with most being somewhere in between. The higher the fur content the higher the quality of the hat and cost. Content is typically denoted by how many Xs the hat is. For instance, a 1x would have less fur than a 4x. Unfortunately, each brand has a different definition of content to Xs. If you have a question you will need to research that brand. Their recommendation is to avoid full felt or wool hats as they become floppy when wet, but some folks like them for the comfort level as they are generally softer.
In photos you will see hats from Resistol, Stetson, Beaver Brand, and Tatton Baird. A great way to find high quality hats for a lower price is to go to vintage shops in western towns. Evan’s current go to larger brim is a vintage Resistol that was a demo hat in a western store in Sheridan, Wyoming that he got at a significant discount, and after a good cleaning and reshaping it looks like new. Shape is what gives a hat its particular style, and there are all different shapes that can be further impacted by brim size and crown height. Another term that you may run into is blocking, which is when a wooden block is used to change the crown height/shape/or oval vs round. Very few “western” shops have blocks so it is best to start with a hat that fits you well and then reshape it to your preference as most hats will not need blocking, just shaping. Both Davis Clothing in Delta, CO and Tatton Baird in Utah have blocking and can help you out. Shaping, hat bands, and stampeded straps give you the further flavor you want in the hat you are wearing.
For the most part you will see Evan wear a lower crown with a pinched telescope (a style he came up with years ago that is his take on traditional vaquero/buckaroo styles), but there are plenty of other photos of him wearing a brown Beaver Brand 3.25" brim fur felt western hat with a Montana Peak crown. Beaver Brand has been out of business for a number of years, but again is a hat Evan found as new old stock and reshaped. Ultimately it was too small for him, so he got the silver belly Resistol you will start to see in photos. For the most part you will see Scot wear one of three hats depending on activity. Two are Stetson “Gun Clubs” with 3.25” brims that were reshaped by Scot to have a Montana crown and had the ribbon replaced with wide horsehair bands. One is brown (back country) and the other bone (town). The third hat you will see worn is a 20x steel grey from Tatton Baird with a 4-inch brim and Montana Peak crown. He loves the hat, but it interferes with a pack and car seat in most vehicles, so he wears it when weather is very inclement or special occasions. Other hats you will see in photos worn by Scot include a silverbelly Resistol with a 4" brim and cattleman crown (Scot’s original FS uniform hat). Time has shrunk it down, but it still gets some wear), and a bone Stetson with a 4.5" brim and a Montana Peak (another old hat from a vintage store).
To get the hat of your dreams, you're going to need to find a decent western shop that knows how to work on hats. As I said above, the higher the number of "X's", the more fur content there is. Scot and Evan's hats ranging from 4x to 20x but shooting for something middle of the road will give you a high quality hat that will give years of use. Resistol and Stetson are good established brands that often have models available in a variety of colors.
From there, you want to figure brim size. A 3.25" brim like Evan is wearing in the photo below is considered short for a western hat but it works well with a pack and in a vehicle. While the one in that is Scot is wearing in back is a more traditional size. Depending on brim shape, anything up to a 3.75" can be worn successfully in a vehicle. A shop that knows how to work on hats can cut a fur felt brim down to whatever width you want. Straw and palm leaf hats can't have their brims cut down.
Next is crown shape. The crown you most often see in the field on Scot is a Montana Peak (mistakenly called a Gus ever since the Lonesome Dove miniseries came out. Ironically, the character Gus probably never would have worn a Montana Peak because it was a northern plains style, not a Texas one). You will see Evan wear a pinched telescope (a southwestern vaquero inspired style he came up with) or Montana Peak. Shaping fur felt hats yourself isn't particularly hard and even hats that have been professionally shaped usually get a little bit of a workover by Evan or Scot. Straw hats are doggone near a one shot and you're done proposition. If you can start with an "open crown" (not ever shaped before), you'll get better results more easily. If it's already got a different crown shape, you can reshape a fur felt. Get a pan of water or kettle boiling on the stove and use the steam to soften the hat and shape it to your preference. DO NOT shape dry as it will damage the hat. Frequent re-wetting is best practices. If you want to get a hat professionally blocked and shaped, we can recommend this hattier: https://tattonbaird.com/ There are a variety of crown styles, just pick the one you like best.
Another small detail that Evan and Scot like on their hats is vents. These are the little eyelet holes in the crown that help with airflow. Finally, they add eyelets for stampede straps. When it gets windy, you'll want one if your hat isn't pretty tight.
The final piece is hat bands, which can be as varied as the wearer. Scot and Evan default to braided horsehair but both also have beaded bands on some hats.
There's your start... have an enjoyable trip down the western hat rabbit hole.