I have both and really liked the juicer but haven't used it since we came out with the citrus press. I L:love:VE the press.
Another vote for the press, although the juicer is great for oranges, which are too large for the press.
I have both--I recently got the juicer. I love the press for lemons and limes but prefer the juicer for oranges or larger pieces of fruit. That being said, I do feel like the juicer actually gets more juice out of them than the press but I do love the press!
Citrus press all the way. Use it all the time at shows on the Pineapple Salsa and Fajitas. Have yet to sell one but everyone is amazed at how much juice comes out and IMO super easy to use and squeeze.
I have both and always use the press for lime and some lemons if they're on the small size. But lately the lemons are so large that I have to use the juicer for them unless I want to waste part of the lemon by cutting them smaller to fit in the juicer. Plus with the juicer you can strain the seeds out of the lemon juice.
Love the press and use it LOTS!!! Regarding large fruits vs small fruits, flesh side down (toward the holes) for small fruits and flesh side up for larger... works GREAT!