The 15x12 is lighter than the 10" Tornado if you ditch the coil cover. I wouldn't go bigger than a 14 or 15" DD coil if you still want to see gains in depth on coin/ring sized targets, because a DD seems to start losing sensitivity to those size targets (costing you depth) around 14 or 15" in size. And even then if the minerals are somewhat present I found on land the 15x12 got less depth on coin/ring sized targets than even my stock 10" Tornado, but for some odd curious reason on my mineralized beaches the 15x12 was deeper.
Concentrics seem to bomb out somwhere in the 10.5" to 12" size range and start losing sensitivity to coin/ring sized targets. DDs retain that sensitivity in somewhat larger coil sizes but there is a limite, based on either the size of the coil or the ground matrix.
For me, having owned a 15x12 and used a 13" Ultimate, if I wanted to pick one for more coverage it'd be the 13" Ultimate. Maybe if I didn't own a 12x10 I'd pick the 15x12, but the 15x12 is too much alike the 12x10 to want both in my arsenal. The light weight and awesome feel/easier coverage of the 13" Ultimate for me is better than the 15x12, but the Ultimate is not as stable in EMI or bad minerals as the 15x12. If I was primarily a beach or open field hunter I wouldn't have got rid of my 15x12, but now I'll take an Ultimate over it just based on it being a different beast than my 12x10 in many respects.
You might also look into the 14.25" WOT coil but it's about the heaviest coil out there if weight is a concern. Detech also sells a 14.25", 16", and I think an 18" Excelarator, and also a 12.5" one same size as the S-12, but you hear little of these coils (Excelerators) so that might say something.