I only have the Lovehoney Deluxe Mains Powered Magic Wand Vibrator, so I'm unable to give much of a comparison for you. However, I think this wand is the best thing since sliced bread and I'd highly recommend it!
I'm not a huge power queen, so I suspect that the Doxy would be too much for me as it's a lot more powerful, but if that's what you're after perhaps the Doxy is the way to go. The LH wand is very powerful and I personally can't use it on the highest setting, although battery operated or rechargeable wands won't be as powerful.
I've heard good things about the Lelo rechargeable wand, which is also waterproof (bonus!), so it could be worth checking that one out too. It looks a lot softer than the other wands, and very glamorous. The LH wands are great but sometimes hard to clean, as they're not waterproof and have a ridged head. The advantage of having a LH wand though is that there is a vast range of compatible attachments for it.
Here's the list of attachments and wands they fit:
Most attachments fit a 7.5 inch circumference head, which I think both the LH and Doxy wand have.
And here's my LH magic wand review if you're interested: