Rickdenham,
You will have to estimate the gallonage based on the use as well as the recirculation. I would allow for a one foot draw down in the spa during maximum use. Then you will need a freeboard amount of water that is always in the basin. I would use a one foot depth of water in the basin for this. I'm assuming you will be recirculating from the basin back into the spa. If the basin is spilling into the pool, then the size of the basin doesn't really matter.
Draw down gallons = 8.75' X 7.25' X 8.5gal/cu ft.

This show what we projected, I'm a little confused by the answer. What is draw down gallons? I understand I need a foot of water always present right?

The simplest way to think about this may be as a ratio. Say for example your hot tub is 70 square feet and your trough is 7 square feet. For every inch of water displaced from the hot tub you would need 10 inches of depth in the trough to contain it. In this example if you expected to displace 3 inches of water through bathers, you'd need your trough to be able to hold 30 inches, plus the 12 inches already mentioned by golfgeek. This is only an example of course, but it illustrates that you really can never make a trough big enough.
Another concern may be the height you propose. A rule of thumb is that the trough should be the same width as it;s eposed height, so if you built a 48" high exposed wall the trough should be 48" wide to contain splash as well.

I'm using the term draw down in reference to the maximum water displacement in the spa. If you have 10 people in the spa splashing around you could loose a foot of water, maybe more. It's better to error building a basin that too big.
Basically, you are calculating the maximum cubic feet of displacement in the spa and then making the basin that size plus freeboard plus a factor of at least 25%.
Is the water in the basin flowing into the pool?

Thanks! The water was going to be recycled back to the spa from the catch basin, but looking at how much space I have, how about if I put several overflow drains above the 12 inches of water, which take that overflow water down to the larger pool. This way, the catch basin does not get overwhelmed.
Do you have any suggestions? Should I just overflow the water to the pool bellow? Will that 10 foot drop be too high, and make too much noise ? Or should I have the drop, then have another step waterfall to the larger pool? I sort of need some suggestions. Thanks so much!!!

Rickdenham,
The plumbing design will be dictated by whether you use a catch basin or just the normal spillway design.
With a catch basin you will need to completely separate the equipment for the spa. If you use a spillway design you can use common equipment.
When a pool/spa combo is in normal circulation mode there is a return line in the spa that refreshes it and causes water to flow from the spa to the pool. The catch basin, by design, acts as the skimmer for the pool(spa in your case) and this water is circulated back up to the spa. Spilling from the spa to a catch basin and then to the pool just makes it a glorified spillway and you can make the basin any size you want.