I own and operate a commercial mowing business. (We do large acreage tracts and highway right-of-way mowing) I use a mix of 15' batwings and 6'/7' single spindle mounted mowers. So I've got a little experience with them and know a few of the subtle differences.
First off, forget about an "across the board" answer as to the differences between 6', 7', and 8' mowers. They vary considerably from brand to brand, and even from model to model with-in those brands. Blade tip speeds, deck configurations, weights, ect, are not consistant from size to size, or brand to brand. And from experience, blade tip speeds ARE NOT the spec that makes or breaks the performance of any given mower. Blade tip speed is a far over-rated comparator. I've owned several with very high blade speeds that didn't do such a great job. Likewise, I've owned mowers with blade speeds that were rated slower than many, yet performed very well. Don't bet the ranch based strictly on blade tip speed numbers. Also, who's to say what speed is "enough" to do a good job? Is more than enough better? Or does it make ANY difference?
From what I've witnessed over the years, deck design probably has MORE effect on a mowers ability to do a good job than blade speed. In particular, the configuration of the rear of the deck. A mower with the ability to allow cut material to clear from under the mower as it moves along will result in better "quality of cut" in conditions other than simply "mowing a lawn". Clipping tops of relatively short grass is about the only time where blade speed is the ONLY real consideration. Be that the case, you're probably wanting a finish mower in the first place.
The biggest single consideration with deck size is usually weight..... Weight in regards to BALANCE of the tractor when the tractor is carrying that weight. (even when not entirely lifted off the ground) Look at the difference between a 5' and a 6' mower. Then look at the difference between a 6' and a 7'er. No comparison. With the extra foot of width comes an extra foot of LENGTH. I've seen several tractors that toyed with a 6' mower and were overwhelmed with a 7'er. They handled the mower just fine from a horsepower perspective. But they required way too much front ballast to handle the weight in a safe manner.
Now...Take that same tractor that had issues with a 7' single spindle mower and put a HEAVIER (but SHORTER) 8' double spindle mower on it. In MANY (but not ALL) cases, that same tractor will handle the shorter deck with ease.
For comparison, I have an extreme duty 6' mower that weighs in at well over 2100 lb. I have a medium duty 7'er that scales under 1500lbs. The 6'er FEELS MUCH lighter hanging on the 3-point hitch of a couple tractors I frequently use them on. It's all about the balance.
Back to blade speeds.... Most brands, especially the "premium brands", will use different gear boxes specifically designed for the mower they're used on. The gear ratios will be engineered specifically to give blade speed and horsepower requirements to fit the mower at hand. That blade speed is often matched to deck design, as well as the probable eventual use of that mower. (ie a mower designed to cut 4" material probably won't end up being used to cut a lawn, or a light duty "economy" mower shouldn't be used to clear a power line right-of-way)
The engineering that goes into a quality mower is why they cost more and perform better in adverse conditions. They're designed and built to do a job, where many lower priced mowers are products of what I like to call "accidental engineering". They MAY happen to work well at a given chore, or they may not.... Who knows?
Back to the original question; Due to length and balance of weight (distance from rear of tractor to rear tip of mower) an 8' double spindle mower will GENERALLY balance better than a 7' single spindle mower. That reduces the SIZE requirements of the tractor. In many cases, size and HP are relative. The benefit of a shorter mower is less of a power issue and more of a weight handling issue.
Finally, I'm NOT a fan of 7' single spindle mowers. Due to width X length, they tend to scalp FAR WORSE than 6' singles or 8' doubles. Not a issue unless you mow close to the ground, but mow shorter than 3" or so, and you'll be cutting as much dirt as you will grass/weeds if/when mowing on an irregular surface.
JMHO, and worth AT LEAST what you paid for it!
A couple of times he mentioned wishing it was about 10' wide instead of 7.
