In 2003 I bought a Braun Silk-epi Eversoft to remove what would amount to a white goatee, (if I decided to let it grow), on my chin.
Even though this one still works great, I believe it's time I start shopping for a new one.
Any suggestions for whats on the market these days that works the best on facial hair?

You can consider getting electrolysis. That way, you'll get rid of it forever without having to purchase new machines. Shaving, waxing and threading are your temporary options. Epilating often distorts the follicles making them curly and causing ingrowns.

Epilady currently offers a machine, called the esthetic, for peach-fuzz type hair on the face that I would recommend. They are also coming out with an epilator for courser hair on the face within the next year or so.... This would be made especially for situations like yours. Hope this helps.