The two programmes have been going head-to-head in the ratings and the ITV1 show, which Dixon maintains is "more entertaining", will move to a later time slot on April 21 to avoid the clash.
"I have watched the show. My family come round on a Saturday night and we have some food and get ready to watch [Britain's Got Talent] and obviously we watch The Voice before," Dixon told The Mirror.
"I am a big fan of Jessie [J], I am a big fan of will.i.am and I love listening to singers so it has been enjoyable to watch."
Speaking of her comments, an ITV source said: "It wasn't the brightest thing to say by Alesha. She is always outspoken but sometimes less is more and ITV and Simon [Cowell] would have preferred her to say less about The Voice, that's for sure."
Dixon also branded fellow judges Simon Cowell and David Walliams "very feminine".
"Simon and David are doing a good job with the camp stuff, we'll leave that to them," she said.
"I think it's going to make for a great live show. People are going to expect the campness from David to wind Simon up and I think he's going to take it well."
The former Strictly Come Dancing judge tipped opera star Jonathan Antoine to do well in the competition.