Well, I never travelled on a Dyna but I travelled all over the country on a Nightrain when I was younger. I liked it quite a bit. Then I learned how comfy a windshield or fairing could be and I was ruined.
You can ride anything anywhere if you have a mind to. I rode a 66 Sportster to New Orleans in one day, 720 miles, a Wideglide 2100 miles in 4 days. You could ride a Honda Rebel coast to coast. But long story short, A Road Glide is my favorite on long or short rides.
Either of your two choices will work for what you want to do if you set it up right. I have a close friend that rode his Dyna, after he changed the seat to something comfortable, along with the rest of us on our touring bikes all over the country. And GNee hangs with us all day, every day on her Heritage without a complaint.
But, as has been pointed out above, if you plan serious touring sometime or sooner you'll be on a bagger.
300 miles a moderate day. Touring usually equates to at least multiple 300+ miles a day. As someone mention any bike will get you far. I know a guy rode an 883 to Alaska from the midwest. Having started on a Sportster when younger and working my way up to an ultra (which i swore i’d never own), the only regret i have is i didnt get ultra sooner. For real touring, the touring class the way to go. From the RK to the sporty street glide and stripped down standard, those big bikes are difference makers for comfort and storage when touring.
As mentioned, both of those bikes can easily be setup for longer rides. The larger bikes just allow you to feel it a bit less at the end of the day.
I did lots of touring on an '06 NightTrain with a comfy seat and a windshield, and my dad did lots of touring on Dynas.
We traded bikes on a few trips. His had more engine work done, so it had a sportier ride, but at the end of the day, the counter-balanced softail had less vibes in the seat, hands, and feet. Of your two choices, I'd chose the softail for that reason alone.