I think DTR balances complexity vs genericity well, leaning well towards the former. Prospective players never fail to mention that they "love the theme" and I tend to think of this as the "easy" entry point. The mechanics is the first hill to climb, followed by the strategy, across all modes of play (piloting, construction, meta).
That said, I think it'd be truly hard to compare apples to apples. Classic had rarity, compounding the complexity considerations with card scarcity. Reloaded sits in a time where there are really great card games competing for hobby-time, and as a result, may not draw as wide an audience out of sheer glut. If Classic were an LCG, or if Reloaded were released 20 years ago, we might be able to make a more fair comparison.
To me, I think DTR retains exactly enough complexity to retain it's best characteristics, while also demonstrating broad enough appeal to not completely alienate all but the most "dedicated" players. The fact that all the "hidden work" playtest does to put a fine point on the work design does is attested to when you look at the comparatively broad spread (across factions, outfits, playstyles) of results from various types of organized and casual play (at least, those who report...).
As such, and double as a fan for complexity, this leaves the soil ripe for Alternate Formats for the hands of those who crave "more" - and their merry-go-lucky playgroups - such that the game can be enjoyed by an even broader spectrum of players. I think the Reloaded team - AEG to Pinebox - have done a great job cultivating that soil.
That all said, do I smell another Alternate Format perhaps called "Harrowed Dominion" brewing? If so, if I were to throw out some ideas, a primary one would be some way for a dude without the keyword already who is killed to somehow obtain it as a result of some effect generated by the format itself. That way, I could use a deck I have already built, not just a deck that happens to utilize the keyword, and participate in the primary fun of the format. This could be accomplished in multiple ways.
Ps. I tease the former Classic players with the phrase "Shootouts are Safe" as a way to use humor to highlight some of the key differences between Classic and DTR. And I think that's actually pretty funny...