Apart from the fact that the "connected" models (HF 3671/3672) have the app and WLAN - which I turn off when I don't need the app because the radiation is considerable and unnecessary - the big difference is the number of programmable changing times. The connected models have several, I haven't tried the maximum number, but you can choose the days of the week (every single one if you want) and have several times per day. The models (HF 3650/01) have only 2 alarm times.
That was my criterion for choosing the "connected" model, plus it has one more alarm tone (I don't know which one), but there are 8 in total instead of 7. I have to admit, though, that I use the APP to programme the alarm times, using the menu is too tedious for me.
You should also know that you have to register to be able to use the app fully, because the synchronisation seems to work via the cloud, because the Connected device has a sensor that detects room temperature and noise and then gives you tips if it is too loud, too warm, etc. in the bedroom. From my point of view, these are things that I personally don't need. I don't think it's very nice that you have to register and I would rate that as a minus point. So if you don't need more than 2 alarm times and can do without the other bells and whistles, then I would go for the HF 3650/01 and save the price difference.
I hope this helps.

For the "connected" models (HF 3671/3672) there is an app with which you can connect to the unit and control it, which is not possible with the 3650/3651 as far as I know. Within these two groups I'm not quite sure either, but I think it's about the colour when switched off.
I have the 3672/01 and it is white when it is off.

Does anyone know if/what the differences are between the HF3671/01 and 3672/01 models? Thank you :)