We are building a basement plus two story 40x44 foot print house in Central Arkansas.  I was planning to use 2x6 framing with spray in insulation however I am seriously considering SIPs now.  Two basement walls that are not exposed to earth, all 1st and 2nd floor walls and the roof would be SIP.  I am considering R Control SIPs that are locally manufactured.

The current bid is based on 6.5" SIPs.  Should I go thicker?  Would the thicker SIPs have additional strength as well as additional insulation value?

We plan to use 18" floor trusses between the floors.  If we go with SIPs then I will install a 3rd set of floor trusses above the 2nd floor to create an attic floor.

Thanks in advance for any suggestions.

I would think 6.5" panels would be fine for walls. I would go with 8.25" or 10.25" for your roof panels. Better insulation value (R30+) and a stronger roof system with less reinforcement required.
Depending on your planned usage of the attic space and clear span, I would consider smaller, less expensive trusses for your attic floor.
Enjoy the experience.

The incremental cost for thicker SIPs is fairly small, we paid a little less than 10% more (about $400) for 8 1/4 vs 6 1/2. There's some additional lumber cost. but I would ask for a quote for the thicker SIPs and see whether you think it's worth it. You can't (easily) fix the envelope after the structure is built, so the little extra up front may be a good plan in the long term.

Depending on your climate, you might want to look at the 10 1/4 for the roof (the 8 1/4 wouldn't meet code here - we need a minimum of R38).

If you want to make a living space in the attic then the SIPs will probably be better and easier than other solutions. If you just want storage, then the trusses might be a cost effective alternative.

When people discuss SIPs they seem to forget to distinguish what skin and core materials their panels are made of. I guess we all can assume you are talking about SIPs with 7/16" OSB skins and 1 lb density EPS core, but if you had a 6.5" OSB SIP with a 2 lb density PU core your R-value would be up around 40 instead of around 24 and have superior strength characteristics. A SIP is not just a SIP anymore, it could be any of about 8 or more different combinations of material. I guess when you say 'R-control' you mean only one thing.