I've played a lot of outdoor festivals and there a huge number of variables that will affect the sound. One of the biggest problems with bass tone both inside and outside is stage volume. When that low end goes all over the stage and into every mic, there are numerous instances of phase difference, each of which creates a smear in the tone. The other issue that if the bass is super loud, then the FOH person is probably a little less inclined to help the guy get heard out front. So, my strategy is to try to keep my level down to a reasonable one. In ears help a lot.
Another issue is that often the tone that the bass player thinks they are getting may be completely different from the one being sent to the house. If you EQ your bass to sound perfect for an SVT and then they take a direct right off the bass, who knows what it will sound like out front?
Another issue: PAs themselves. We live in the era of the line array. There are lots of things written about it, so you can surf to your heart's content to find out about the implications of it. The bottom line is that it creates a very efficient and controlled way of getting the sound to the audience. It results in a smaller truck pack and less electricity usage. However, there's something about the mids and highs that to my ear create a kind of mp3 effect. I've never heard a line array system create the sort of impact and depth of sound that was available in the old school systems. Maybe it has more to do with the switching power amps of today than speaker technology, all I know is that I find them fatiguing and unsatisfying to listen to. The exception is the line array for the low end. However, this requires a set of subwoofers 1 wide and 40 feet ( at a minimum) tall. The theory is that your stack needs to be taller than the wavelength of the lowest note you want to propagate. With a low B being at 30.87hz, you need a stack 36.417 feet tall. This changes the physics of how the wave propagates. Instead of it propagating as a segment of a sphere and falling off according to the inverse square law, it propagates as a section of a cylinder and falls off linearly. The efficiency, impact and depth of such a low end rig is simply stunning. It sounds like the bass is coming up from under the ground, yet is super quick and has incredible impact. I've only heard this in person once. The rig had two very tall stacks of Meyer subwoofers and it was a profound bass experience where every nuance of the bass guitar had a practically three dimensional clarity to it. However, it probably required almost a whole semi to cart the thing around.
Mike, in the end, is right, though. Not only does the sound primarily come from the fingers, but what you choose to play. A really cool lick with a million sixteenth notes will get lost in the inertia of moving the air along with the other instruments, whereas a really well thought out and relatively sparse line will be perfect.
Of course, if the FOH guy is one those guys who measures his privates by the size of his kick drum sound, all bets are off.