Some of the problems of live sound mixing inside are reflections and the standing waves created by the dimensions and shape of the rooms and the position of the stage in the room. This changes with an outdoor venue. There may be few or no reflections with an outdoor stage. If there are reflections, there is usually a much longer delay before they return to the stage. Sometimes specific frequencies will reflect from some surface but other frequencies will not be reflected to the same extent.
Often there will be less problems with feedback on an open outdoor stage. If there is a roof it is usually higher than in a club stage situation. Also there may be no walls or just a back wall to reflect sounds back to the microphones. Inside stages with close walls and ceiling can reflect sound back to the microphones whereas outside this is often not a problem.
There are likely to be cancellation and reinforced areas that are dependent on speaker location. These will be more predictable with outdoor sound. If you use a stack on either side of the stage including subs there will be strong low end in the center of the venue but there will also be cancellation points off center on each side, usually between the center-line and the stacks. From a position directly in front of either stack you may hear the actual balance of the mix.
What is needed for Outdoor Shows
Depending on the style of music and the volume desired a sound system may require more power and more speakers for an outdoor show. You may also need to mike some things that are not needed in a club venue. Outdoor stages are often bigger than the stages in clubs, so you will not have as much bleed into the vocal mikes and other live mikes on stage. If you have the proper equipment it is easier to mix outdoors because you are not fighting the sound problems inherit in a room.
You may need to have an input from each instrument as well as your vocal mikes. You may also find benefit when working out doors to put up overhead mikes on the drum kit. Cymbals may bleed into vocal mikes on a club stage but may be lost on an outdoor stage. Also miking each individual drum will give you more control if you have the mikes and channels available. Guitars and keyboards may need to be in the mix for balance and dispersion. Many guitar cabinets tend to be beamy and the sound can drop off axis often dependent on frequency.
The monitor system may also need to be stronger for a large outdoor stage. Musicians may need more things in their monitors for timing. More monitor mixes are also desirable for outdoor venues. Usually for events other than concerts four mixes will work well. A stage right, center stage, stage left, and drum mix will allow you to give the musicians what they need to hear in most cases.