The .338 Woodswalker is an excellent cartridge. In my 10" barrel, I run both 180 gr.Nosler BT's and Hornady 200 gr. Spire points, with very good accuracy. Unfortunately, the excellent 200 gr. Flatnose, intended for the .33WCF, and which was perfect for this cartridge, was dropped by Hornady about 5 years ago or so. A 200 gr. can be run @ 2000 fps from the Woodswalker, but the gun and shooter are a bit happier @ about 1900 fps.
The original .338 JDJ was on the .303 British case, is obsolete and is not worthwhile.
The .338 JDJ No. 2 is on the .444 Marlin case, runs a 200 gr. Hornady Spire Point @ ~ 2300 fps and is absolutely outstanding in accuracy and lethality, fully the rival of the .375 JDJ in usefullness.
If I wanted a 10" barrel, I'd pick the Woodswalker and I'd be happy; If I wanted a 14" barrel, I'd pick the .338 JDJ No. 2 and never look back.