I have the Silhouette. And the Big Shot.
Manual Die advantages -- the result is a more finished edge -- often rounded down. Looks nicer (but I often get a dirty mark if I don't use wax paper). And some, like Spellbinders, produces the beautiful embossed edge. Faster if you only want one image.
disadvantages -- money, storage, limited to size of die, time consuming if you want multiples of one image.
Sihouette -- LOVE this machine. I can make multiples of tags, change the size and shape of any image, make my own images, cut out any size letters in any font I have, make words, make any shaped card, etc. I just LOVE this machine. The best money I've spend on papercrafting in a very long time.
However, it isn't perfect -- no machine is. It can be wonky, sometimes the cuts are not clean and there is the cost of blades and mats. Nothing is free.
It's personal preference. I don't see myself buying a lot of dies in the future.
Stamping and a serial novel, "How Stamping Destroyed My Life"