Lots of Pro’s and Con’s, do and don’t. But it depends on the bike and the rider.
I think it was Top Gear or Fifth Gear that did back to back tests with three types of car, three types of fuel. Supermarket, Regular and High Octane, the BP and Shell variants. The lesser fuels don’t warrant mention!
So … small engined compact hardly any difference on the High Octane, family car slight improvement, performance and economy, WRX and Evo 35+ BHP !!! 
Performance engines (particularly cars) do read ron (octane value) and compensate to use it to the Max.
If I want to go out and blow the cobwebs out, I treat the bike to the best octane and on my 04 R1 it gives between 8 - 10 bhp depending on what I put in. We have a Dyno and have seen the difference on the graphs but with the R1 I can feel it. Its ‘Yeehaa’ as opposed to ‘Way-hey!’ It’s like putting a free breathing can on, you get an extra boot in the ar*e. Like on an summer evening when the temperature drops and the engine runs so sweet its flying. I can feel it in how much easier the front comes up. When I don’t use it the motors feels as though its gone off tune.
Something else that has the same effect (but les BHP) on older injection motors is injector cleaning fluid*, (Redex etc) it has something in it that boosts power for sure, in petrol engines.(* Recommended regular treatment on injectors over 5,000 miles) 
If you are not going to ride the bike in the top half of the rev range you are wasting your money. When we ride out we set off gentle to get everyone into the groove, so I put in regular fuel, on the way home we usually have a blast and I’ll have refueled with High Octane.
I have had the higher octane left over on occassions and ridden steady, I have noticed an improvement in economy then.
I always use the High Octane on Track days but forget economy … in fact I’ve look for leaks before now it disappears so fast. 
One last thing, its not just an urban legend that Supermarket fuel lacks a little something to get the prices they do. Refineries mix to order and cost, the mix varies from week to week. Better built engines Audi, Mazda etc) and performance motors don’t perform as efficently on some of this cheap crap … so it has to work harder at the wrong temperatures. Not good.