The Bowie with escutcheon has a walnut handle and the other a cocobolo handle.
Moran's standard handle material for this model (and many others) was Rosewood. He was noted to occasionally mention "dark Rosewood." Whether this was naturally dark Rosewood or dark stained Rosewood isn't clear.
Customers could request different handle materials but the only options mentioned in the catalog wherein this model was listed were Curly Maple, Ebony and Lignum Vitae - all at a $6 premium, except for two piece slab handles which ranged from $12-$24 extra depending on size. Inlaid Sterling Silver Shields were $12.50.
I did find elsewhere a reference to Walnut as a handle choice for no extra charge - likewise Hickory though Moran felt Hickory offered no inherent beauty and only used if if requested. I find no reference to Cocobolo during the time frame in question though that doesn't exclude its use.
From the photographs posted I personally can't determine the wood type with certainty and therefore trust the owner's judgement on this.
I would suggest looking carefully for sheaths made by Moran for these knives amongst the other items in the safe(s). Moran's sheaths were expensive for their time, but very well made and naturally enhance the value of any Moran knife. Additionally, paperwork such as the brochure/catalog and/or price list pertinent to these knives would also increase their value significantly when considered as a package - 2 knives, 2 sheaths and documentation would be a truly great find!
I highly recommend getting a copy of
Master of the Forge: William F. Moran, Jr. and his Classic Blades by B.R. Hughes and Houston Price. Knife World is my preferred source for all knife-related books:
http://www.knifeworld.com/ It is a truly amazing book with interesting text, many quotes by Moran and photography that is mind-blowing for the pre-digital era. The vast majority of the knives featured in Master of the Forge are truly mint blades. Anyone who is of the opinion that Bill Moran produced what was essentially folk-art quality knives will believe differently after perusing this wonderful book.
Many people favor Moran's ST24 model but if I could have my choice it would be one of his fancy daggers: The Cinquedea, European Stiletto, Poignard, Quillon or Viking Dagger, with Damascus steel, naturally.