If you go with a 2.0" coil over, they are more valved for street and slow off road. Those are generally a little more plush on streets.
The 2.5" coil overs are generally more valved for off road, and if you read icon, king, fox, etc. 2.5" reviews, a lot say they are more harsh on road but amazing at 35+ off road, which is their design.

Better ride is subjective, a lot say they do give a better ride due to other factors like less body roll, a more planted feel, no wandering, etc.

You could try lowering the coilover collar a little to not compress the spring quite as much. This will give you a little more of a plush ride with the sacrifice of front lift height. If that doesn't help, a spacer designed for your lift kit (the stage 1 option) and using your factory coil over will give you back your factory feel, that would probably be your cheapest option.

There are many factors that can go into a coilover. A big one is spring rate, which the aftermarket is probably using a 650-700lb/in eibach spring (most do) compared to factory which I believe is around 450lbs/in. Then depending on the valving on how it allows the fluid to flow determines a lot of the characteristics of the coilover. I know bilstein's are generally are a little stiffer ride but I would consider them better because it fixes a lot of the looseness of the stock suspensions. I am putting fox 2.5's with dsc (Around $2k) on my truck here in another month and have read quite a few reports of a similar thing as the bilsteins. Same with Icon and king when I was researching. Now the 2.0's I have read that they improve street performance for the most part., but I am building an overland rig so I value the off road performance and am willing to give up some street comfort.

I don't know much about and have never experienced the pro comp coilovers, but when I searched pro-comp coilover reviews, the ones that actually talked about owning those coil overs complained about it being a very harsh ride. A 2.75" coilover for under $1000 (after coupons etc) doesn't breathe a lot of confidence in me that it is very good.

But again, I would try backing off the spring preload a little (if you can) and seeing if that helps, it probably will.

On my motorcycle (penske double clicker with remote reservoir) which has rebound and compression adjusters (Which control oil flow), I can make the ride cushy or as hard as I want by controlling that oil flow. It also has a spring that was selected for the machine and my body and gear weight. For more aggressive driving, I want it a little stiffer. For general commute, I want it a little cushier. But when I am riding aggressive I don't want to bottom out my suspension in a turn. That gets scary. My commute doesn't have me pulling fast turns so I am not worried about bottoming out as much.

Same with my my rzr with the fox shocks. Factory setup wasn't great. Spring rate was terrible choice and valving was off. I changed the springs to a dual rate setup and had the valving adjusted to match my machine and riding style. Now it is a Cadillac off road going over massive bumps. But On streets it feels a lot of the small bumps (the shocks are made to move throughout their range, not just a tiny bit), super loose from how I have it set up, and can be dangerous (I really limit on road for many reasons but this is one of them.) I also have compression oil flow adjustment and can make it softer or firmer by controlling the oil flow as well. I firm it up when I am going to be going over massive bumps and quick so it doesn't bottom out the suspension. When I am cruising slower speeds or flatter ground, I soften it up.

Moral is, it depends on how these are setup. Most 2.5"-3" coilover are designed to be off road beasts and are valved and sprung as such. They don't absorb little bumps well because they are designed to not bottom out on the big bumps but take those big bumps in stride and feel the same on big bumps as they do on little bumps. They are also that size (2.5"+) so they can hold more oil and not fade as quick as the oil heats up, also why reservoirs are used, more oil.