I have practiced Druidry for over 15 years..before that I had a hand in Wicca. I'm going to give you my opinion on this...
Wicca is more magi ck based, while Druidry is more nature based. Yes, I know Wiccans are nature-lovers as well, but Druid magi ck stems more from tree lore and is based within the Celtic pantheon. Wiccans can chose from various pantheons when doing their spell work.
Druidry also believes in necromancy while some Wiccans shy away from that.
Both believe in 8 holidays in their respective Wheels of the Year, while Wicca refers to them as Sabbats, Druids call them Grove Festivals. And the names vary somewhat, as much of traditional Druidry names come from ancient Welsh/Gaelic.
There are many differences but in reality both are nature-based religions and both have been around since before Christianity. They are both able to be labelled as 'Old Religions'.
I could go on for a while, and if you need any further information please feel free to email me your questions. I'll help with what I can.
Good luck!
Also, one more thing - Druidry does not have a 'Rede' like Wicca does, but we have an established system of Triads that have been passed down from mentor to apprentice for years.