Two lengths of 12/2 romex to substitute for 10/2
You only need one run of 12/2, so why waste money?

12/2 is already legal for 20A so you're all set.  

At 100' you will have 0.2% voltage drop per amp, or 4% drop if you redline the circuit at 20A, which you should not do, as a rule; you should only plan to run 16A (80%).   You do not need a wire size bump for voltage drop at 100', and your run is actually 65' so you are all set. Figure on 0.13% voltage drop per amp. So at 20A 2.6V drop, no big deal.  

For anti-dimming, use LEDs or fluorescents with modern ballasts

Specifically look for LEDs or fluorescent ballasts made for multi-voltage 100-240V (world voltages).  Those will automatically adjust to voltage "on the fly" so dimming will be minimal/nonexistent; the device will simply treat a startup sag as "oh, we're in Japan now ok". 

Common 15A receptacles can only be on 15A or 20A circuits.

As soon as you put a 25A or 30A breaker on it, you can't have receptacles anymore.  Unless you feed that circuit to a subpanel and distribute it to one or more 15/20A circuits. 

Every breaker is dual thermal/magnetic.

They all have a permissive curve allowing some seconds for a 200% load, some minutes for a 1.25x load, and instant trip for a 1000% load. 

If you want that feature local to the shed, feel free to install a subpanel. This can be fed with 120v (mine is). You can then use a 30A breaker to get full use out of the #10 wire, and local breakers of appropriate sizes for the circuit.  Subpanels are as cheap as $20 and breakers are typically $5 if you're not subject to AFCI/GFCI requirements. 

There can be only one

One NEC rule is that you can only have one circuit of the same type and usage.  So sticking two 120V circuits out there isn't allowed, unless, say, one of them is controlled by a light switch from the house.   

However you can have a 120V circuit and a 240V circuit, 120/240V split-phase circuit, and an MWBC (all at once even). 

So have one of your two 120V circuits switched from the house.  Or run a larger 120V circuit and have a subpanel.  Or run a 120V/240V circuit and have a subpanel. Or run a MWBC.

Wait, what's a MWBC?

It's 2 hots sharing a neutral.  It must be punched down into a 240V common-trip breaker, you can't use a duplex/twin or you'll overload the neutral.  

Say you run 12/3 cable and punch it down onto a 240V 20A breaker.  You now have 2 full 20A circuits worth of power available to you.  YOu split one 20A/120V circuit off black and white, and the other 20A/120V circuit off red and white.  Great for saw on phase 1 and dust collector/lights on phase 2 for instance.