Your efficiency will depend a lot on the lautering ability of your mash tun. The more uniform the filtering the more efficiency you'll get out of fly sparging. This is why most fly sparges are done with false bottoms or with manifolds that cover a good portion of the bottom of the tun. If you are just using a braid then you're not likely going to increase efficiency.
For homebrewing I'm solidly in Denny's batch sparging corner with one caveat... big beers. If you try to batch sparge a really big beer, your lautering efficiency drops like a rock (assuming the mash tun size remains the same). There isn't a lot of data out there on batch sparging big beers for lautering efficiency. There's plenty of conversion data, but we're assuming that you get the same conversion % with either method and any size batch. The reason that there isn't a lot of data is because everyone's equipment profile is different. Most of the equipment is a hodge podge of whatever fittings and crap you can piece together to make it work on the cheap (as it should be). So collecting data for yourself is paramount in being able to predict what your efficiency is going to be when you make a big beer.
With my homebrew set up if I went over 1.055 I was guessing what my OG was going to be. After a lot of batches I started to learn approximately what the OG would be, but it was still a crap shoot. DCRIPA at 1.075 was down in the low 60%'s. That's really friggin annoying when you can't predict your OG right and you miss your OG.
How do you fix this? Either sparge a time or two more (batch sparging), use a larger vessel to batch sparge in so your grist ratio remains the same (Theory of mine - I never tried it), OR fly sparge.
The nice thing about fly sparging is that your efficiency should be independent of your batch size. You can make a big beer with a lower grist ratio and you ought to be able to get the same lautering efficiency every time (again assuming your conversion efficiency is the same).
Edited by SchwanzBrewer, 02 February 2016 - 01:38 PM.