I have used many full beds of shaped polys (Savage Black, Black Widow, Cyclone, Black 5 Edge, BHB7, Alu Spin, and many many more). I have also used round smooth crosses with some of these shaped mains. I have tried Polylon, Revolve, Black Zone, Alu Power, and a few more.
What I have noticed is that there is no clear-cut answer. Some shaped mains responded well to smooth crosses while others felt terrible. I love Savage Black in a full bed but hate it when it's crossed with a smooth poly. As popular as BHB7 is, I personally find it too plasticky and unpredictable in a full bed. When I used Black Zone as a cross with BHB7 mains, I suddenly found a huge jump in spin, bite, and control. The feel was closer to what I enjoy in a full bed of poly.
I suppose the strings' stiffness and material had a lot to do with it.
After I became addicted with trying new strings, I noticed I had a pattern. I enjoyed softer mains and stiffer crosses when using a hybrid. I hated having stiff mains and softer crosses. Some people are the complete opposite.
This could be beneficial for you if you know what you like. If you want to have a full bed of the same string, you can adjust tension in the crosses to get stiffer or softer crosses. Of course, you can leave it the same. Same option goes for using a different cross. You can adjust as you like depending on stiffness or whatnot.
Now if the strings are offered in different gauges, you can fine tune further for power, feel, etc.
My favorite full bed of shaped poly: Savage Black with same tension mains and crosses. My favorite shaped/smooth poly hybrid: BHB7 16 mains and BZ 17 crosses with same tension mains and crosses.
You're going to hear it a lot on these forums... every user has a different experience. With that said, I'd say choose your favorite shaped strings and use it in a full bed and a hybrid. Test it out for yourself. You can also choose your favorite smooth cross. I prefer Black Zone as a smooth cross as I feel like it has good tension maintenance, slick surface, and on the cheaper side.
Since every string responds so differently, it is difficult to comment on which has more spin, control, and durability. But with my limited experience with full beds of BHB7 16 and my BHB7/BZ setup, BHB7 usually lasts me around 30 hours (before it breaks) compared to BHB7 16/BZ 17 which usually lasts me 15 hours. However, BZ was 17G. I found more spin and control with the hybrid setup by a huge margin. But like it's always said on these forums, every user has different experiences. I hate BHB7 in a full bed but a majority of people find it awesome.
Experimenting and finding good setups is part of the fun! Go buy bunch of strings and enjoy it! lol