Is there a significant difference in the tone between these two or is it more subtle?
Those are very decent guitars but totally different animals than the Martins. My pick for Yamaha would be the LL16. It's more money but a whole lot more guitar too.Obviously my tastes may be different than yours but I bought two acoustics in the last few years and did a lot of testing.
I like rating things and I gave the Martin DX1RAE 2.75 out of 5. I gave the DX1AE 3.5/5. I gave the Martin D-28 a 4.5/5. I gave the new Martin D-18 a 5.
If you want to save some money I gave the Yamaha FG800 a 3/5, FG820 3.75/5 and a FG830 4/5.