If you have two breakers of the same type, the one in the house is much more likely to trip, because current is pulled through that one to get to the other one. Breakers trip on heat, so it's a race between the two, and the one feeding the second gets a head start.
There are other things to consider, too - it's generally a great idea to run power tools from a GFCI protected receptacle. This saves you if something goes wrong with the tool causing parts of it you might touch to become energized.
What I recommend you do is run a new 20A circuit to your shed for convenience receptacles, and make sure to use a GFCI receptacle (you could go for a GFCI breaker, but you're back in the boat of having to run inside to reset it if it trips). This allows you to install even more receptacles from the load side of the GFCI for convenience, and makes things safer overall.
With what you have, you're good for lighting and probably some chargers for cordless tools and such, but any circular / reciprocating saw is going to trip it if it binds (and gets closer to the listed locked-rotor amperage).
If this means some digging, you could also go for a 30A sub panel in the shed that would meet current and future needs (any time you dig, it's good to future proof a bit, makes the time spent trenching more valuable). There's no real good way to fix this without heavying-up what you've got.
A great way to plan for what you've got is to take the LRA (locked-rotor amperage) of the biggest motor you intend to power and multiply that by 1.25. In this case, it's going to be either your compressor, or possibly circular / miter saw, depending on what you have. This should be stated on any UL listed tool.
For most household compressors, you're going to end up somewhere around 24 to 27 amps pulled if the motor is energized and completely seized, so a 30 amp sub panel would probably be your best bet to run a few tools at normal (non-locked) operation, while providing some allowance for blades binding a little, or the compressor recovering pressure while other things run.
But, run the LRA of the stuff you want to use together typically, and you'll get a pretty good idea of what you'll need to pull out to the shed to support it. Your normal continuous load won't be nearly as high as the LRA, but you've got to plan for the occasional peaks.