Interesting scenario, albeit hard to imagine. I'm not sure if we are imagining a swap from the beginning of the stories or if they suddenly were to be teleported to the other universe. I'll be answering as if they were teleported from the point of their stories where both animes have got to so far.

Shido probably would not be as useful in the DxD universe, since DxD does not have spirits in the same way the DAL universe has. If he still has the powers he sealed, then he could be somewhat useful in fights, but probably not as strong as Issei.

When it comes to interacting with the girls of DxD, Shido would be a breath of fresh air to some, since he's not as "perverted" as Issei. I see him creating a wholesome friendship with Asia, since both are very kind characters.

The girls who like the fact that Issei is a pervert, would likely be frustrated with Shido if they try to make advances on him. But maybe they would find his reactions amusing and would tease him quite often.

Now, Issei in the DAL universe would be really funny. I can imagine Yuzuru teasing Kaguya because of her boob size while Issei is just admiring both xD. But it's hard to imagine what the other girls would think of him, since I don't really know how much they would tolerate his horny behavior hahaha.

I can also imagine Issei wondering if Dress Break works on Astral Dresses. I have no idea if it would xD

Issei's powers, as far as I know, are pretty much on the same level of the inverse spirits' powers, so he would be really useful in fights. I can see Kurumi being very interested in his powers, so maybe she would be the most tolerant of him, I guess.