So which one do you book? It comes down to what you want to remember.
The eastern route is the one for capitals and mountains in the same week: three old cities, a spa town, Hallstatt and a glacier, with the final two days doing most of the scenery. It is also the cheaper of the two.
The western route trades peaks for cities you have known since school. It slows down in Paris, the drives through Belgium and the Netherlands are short, and the beds are four-star.
Pick East For Variety
Take the eastern loop if you prefer seeing a lot of places well enough to talk about them to one place properly. Old town squares, the Hungarian Parliament, an alpine lake and a cable car above the clouds all land in the same week, and you never unpack twice in a row.

Pick West For Cities and Food
Take the western loop if Paris is the reason you are coming, or if beer, chocolate and cathedral squares matter more than altitude. It is also the gentler week physically, with four-star hotels and a Paris day that happens on foot.
Departure Days and Joining Points
Your calendar often settles the argument. The eastern route leaves Frankfurt on Mondays or Wednesdays depending on the version you book, and it can also be joined in Prague, Budapest, Vienna, Munich or Zurich. The western route leaves Frankfurt on Saturdays and picks up in Paris, Amsterdam, Brussels, Cologne, Heidelberg or Luxembourg on other days.
Traveling alone is not a problem on either. The two eastern departures offer free room sharing, which keeps the single-room supplement off the bill. The western loop lists a shared room as available instead.
If a week feels short, you can add the western week after the eastern one. The eastern loop ends on a Sunday evening and the western one leaves on a Saturday, so the plan comes with several nights in Frankfurt between the two.