Flash technology provides a much richer experience than an animated .gif or static image for the user when utilized in web advertising. It contains in it the technology to enable multiple functionalities, which can bring the experience of an entire website to the user with just one impression. Forms, games, product features, etc. can all be experienced without leaving the current website. Animation is also a fantastic way to draw the eye on a static page.
However, in the words of Uncle Ben, "With great power, comes great responsibility." As a web advertiser, it is your responsibility to grab the attention of your audience and get your message across before you are passed by. With all of the power, potential, and freedom flash has to offer...you can do just about anything in an advertisement. You need to find that balance of design and functionality.
What is the function of your ad, what is its real objective? Branding? Information? Distraction? Media experience? Click enticement?
Users navigate the internet in fractions of a second. Not minutes, not seconds, but fractions... When a page loads, you need the brunt of your message on screen, or at the very least something so compelling that the ad becomes a focal point. If your file is too large or there are too many elements involved, the ad may not even load before a user scrolls past it or moves on to another page. If there are multiple ads on a page and someone else's loads quicker and compels a click from the user... It doesn't matter how amazing your design is or how much experience your ad has to offer, because you just got beat to the punch.
With this, you also have to consider length. Web users get bored easily. If your flash ad takes forever to get the brunt of its message across, they'll pass it by and there goes another wasted impression.
There is always a correct tool for every job. You need to evaluate your campaign objectives before choosing a side, but in my opinion design trumps everything in advertising, not technology. If you have the skills and the eye for it, and your message can be broken down simply enough, you may be better off using a simple animated .gif or static image as your canvas.
If it's a multimedia experience you are looking for, flash is definitely a fantastic tool, but always keep your objectives in mind. If a web advertisement never gets its message out in time for a user to see it- does it really advertise anything?