It's really more a matter of how large your projected image is rather than distance. You're concentrating the illuminating passing through the slide over a given area. With a wide lens at a short distance covering the same screen area as a long lens at a large distance, the image will be approximately the same brightness. Both digital and slide projectors have a wide enough range of brightness that you'd have to be specific about models to get any relative brightness information, and you'd also need to be specific about the ambient light levels you're trying to overcome.
Projector lenses vary widely in quality, from plastic zooms (and zooms are typically slower than fixed focal lengths) to great fixed length fast lenses with excellent glass. If image quality is a concern, you'd need to factor that in. Schneider, Zeiss, Leitz, Buhl (in the US), among others make excellent slide projector lenses. Wide angle slide projector lenses are rare. Usually a 90mm or longer lens works for the majority of common slide projection setups. Also, with a short lens, you'll need to have the projector closer and tilt it more to cover the same area, leading to 'keystoning' in the projected image, i.e. the bottom of the image will be narrower than the top, and the sides will fan out going from bottom to top.