What is the GPS logging app du jour for tagging your photos in Lightroom?
I think the best iOS app is gps4cam. It can log accurately, and some of the parameters are adjustable. It has a companion desktop application, and all you have to do is take a photo of a QRCode and then the desktop app finds it and geocodes your photos. No GPX files to import; in fact nothing but the photos. It also works with HoudahGeo, which gives you more control over fine tuning locations, writing to files, etc. It's pretty amazing how they get all the info into that QRCode. Then just use "read metadata..." to get it into Lr.
In response to the OP, GPS loggers in general aren't very Mac friendly, and many don't work with iOS. But some do.
Accuracy kinda depends. The latest chips help, and so does the antenna. Reception is pretty key; in general new ones will be better than an iPhone in many situations (see here:
http://fulcrumapp.com/blog/gps-accuracy-experimentation/).
But accuracy while moving can be an issue too. If you need something that can keep up with a fast moving object (like a camera mounted in a car) then a higher refresh rate can help; 10hz is probably the most feasible consumer unit right now, like the XGPS 160. It's used a lot with car geeks on the track. iPhones don't keep up very well. It's also a nice unit cuz it works as an external for iOS apps, and can data log. It's got a 10 hour battery but can run on a 12v connection.
I've use a GlobalStar BT 335, but it's a pain, mainly due to poor Mac support. I prefer my iPhone when I can, or a dedicated GPS unit like a Garmin (which I have for other purposes, not just geotagging).
One issue with dedicated units to be aware of is acquisition time. My built-in GPS in a Panny takes forever; you just sit there waiting while the animals slowly move out of range. Then hang around to take an establishing shot to get the GPS. Some units are better than others, but with some loggers you pretty much need to leave 'em on. If you are stopping and taking photos at one spot for a while, it's sometimes better to just use an iPhone that's got BT and wifi and cell turned off; take a photo to capture the location and just copy from that later.