i didn't see the first iteration. not sure which is which, but for the first i'd say stay away from drop shadows, and those outlines are overdoing it (less is more). it looks like the "II" is squished between the Rs as well. beyond that, it's not very memorable imo, i'd suggest distinguishing it with some sort of relevant graphic/symbology (something tasteful--for instance, a crown)

i think

i'm not really qualified to give advice on typefaces but check around dafont for another serif font, or modify it yourself in inkscape (or your preferred vector graphics software). i'm saying that because the straight section on the Rs look kinda wavy and it's throwing me off but that could just be me. i also think the bottom font isn't very unique, and it's a bit too bold. subtitles shouldn't distract from the main graphic

if you still want an outline, then try making the edges more square. round outlines on hard edges and corners don't play well. the only problem with the color choice is that you can't just give the letters a black outline, because that'll just give the first R more weight. i can see why you tried to make a smaller white outline inset from the black outline. maybe try decreasing the weight of the outlines and cleaning up those edges so they aren't round

it's a learning process! you'll get it, it usually doesn't come naturally. the top is a significant improvement over the bottom that's for sure