I'm going to assume you have a favourite game. Mine is Domaine. BTW, I haven't played Lowenherz, so I am unqualified to get into that discussion. However, here's a question that's disturbingly difficult to answer: why? Why is your favourite game your favourite game? What's so good about it? Let me speak for Domaine while you think.
Firstly, there's not much luck. The random set-up does add some luck, unless you are skilled enough to analyse the board and choose an optimal start position, but I am only good enough to choose a decent one. Also, the cards add some randomness, but with the chancery there's a reasonable chance you'll be able to get any card you need at some stage. Overall, the cards seem to even out.
Secondly, it's an economic game, so you have the chance to develop your economy in order to fund the war effort, and I like that because unbridled aggression and rushing don't work. Furthermore the economy and the war interact (if you lose mines, you lose money), so you need to continually maintain your economy.
Thirdly, there's conflict, but not too much. I don't mind conflict between players, but I don't really go for games where everything that is good for me is bad for you, Memoir '44 being a notable exception. In Domaine, there is always the chance that a player could attack you, but you have the chance to make it too difficult or not worth the effort, so you're not perpetually fighting people off.
Fourthly, there's cooperation. Few domaines are built by one player's walls alone, so the first part of the game is sort of cooperative building of the domaines, with a little bit of squabbling about where the borders go, but not too much or else nothing will get built at all.
Fifthly, there's thinking. I like games where I am always thinking. Tikal, Louis XIV, Trias, all get good points for that. There might be down-time in Domaine, but I don't notice because I am thinking what I need to do next, what is he doing that is a threat to me, why did he just take that defector card from the Chancery? Shadows Over Camelot and Citadels are otherwise good games which just don't inspire that sort of thought in me.
Between the combat and the thinking, there's perpetual tension. I am always thinking how can I complete that domaine, is he going to attack, am I going to have enough money, am I vulnerable anywhere? It's good stuff.
Lastly, I am at least a little bit good at it. I admit, I don't think I've ever played against an experienced player, but I usually win and I know what I need to do and I have a fair idea of my chances of success. Often, my plans work. There are fine games such as Samurai and Alhambra where I can form a plan, and it never helps. At least in Domaine I play well enough to always be a contender, and if was to lose I'd be able to identify causes.
I was just considering a posting about my least favourite games, but I haven't got the time to express my passionate hatred...