No real difference in home play. The main difference is a digital clocks ability to have time increments, time delays and some other tournament features like bonus time given after 40 moves. But again no real difference if you're just playing at home. I would say get the analog clock who's aesthetics you like best. Garde, and BHB have fairly iconic classical analog looks.
Analog vs Digital clocks

There’s a classical ‘romance’ to an analog clock and I’m glad I have one but like the phone I am typing on compared to my analog watch …digital has more options - whether you use the options of not … that’s another question.
If I needed a click - and didn’t have my BHB’s, I reckon I’d go digital - something like a DGT3000 with faux wood case.

You'd have to buy both kinds, one bringing home the historical beauty and one with the beauty of the increment. Do take two. If you got one, for the second you are in no hurry.
Here are three of the most popular analogue clocks in Germany, the small bhb (v.Rolland and alpha produced clocks of this compact type, as well), the laid back Jerger and the great big Garde.
These three forms saw many editions. Widely used- and now, with clubs letting their analogue stock go and with analogue clocks in private hands being given to the younger generation, they are widely available here.
Generally speaking, the older the edition, the more beautiful: more wood (sometimes bakelite) and metal and less plastic. The older the clock, the more likely it is it will need a cleansing (then again, some have already been cleaned in their life). That could easily double the price, but okay, it is worth it.
Analogue beats digital in looks and sound- the ticking and the clicking of the metal buttons on wood is marvelous. The digital silence may be fine. The ever changing digits- they are what they are. The plastic plopping of the see-saws, for sure, is alienating.
Strikingly, however, digital clocks offer increment- the addition of extra seconds for every move you made. In blitz that could be 3, in rapid 10, in classical 30 seconds increment per move, for example. That makes so much sense, because you get a timed game, but flagging as a strategy does not work any more.
Garde had produced a digital clock in their classic style, housed in wood with metal buttons- very sought after today. For me the mix looked goofy. I like the zmf-2 and chronos clocks, touch or button, even though they cost a lot more than some of the clocks with plastic see-saws. (But even the ploppiest seesaw brings you the increment).
When I play casually, I use digital for blitz and rapid to enjoy the increment- and analogue for longer games like 35 minutes each or more, for the beauty of the looks, sounds and handling of a good old clock. If you decide to have only one clock and it's analogue, mind that the flag, while a clear mechanical solution, is hard to read- you have to learn to estimate your seconds remaining towards the end of a game correctly. If you intend to play mostly short time controls, take a clock with a bigger face, like the Garde, because it is easier to read.

Digital is more practical and useful, and precise.
But Analog has the thrill of the sound, the retro feel, and the flag, which drops which you and your opponent have to watch when time is short. There is a purity in the analog, in the stress the little flag causes.
But ultimately get whatever u like!
I want to get a good clock for home play but I’m not sure if I want analog or digital. Digital seems easier to read and control but I like the look and classic nature of analog. What’s your preference? Why choose analog over digital? Which classic clock is the best overall for play?