Or is it more like London buses where the state sets and collects the fares, and giving contractual money to the private operator ?
It's done like that on a Gross Tendering basis. The regional state government pays the operators directly (mostly on a per route basis), and the local 'PTEs' set the fares on local/regional services in their area. Almost every area (regardless of whether it's an urban area or not) is covered by a PTE.
You must've been lucky then, as DB's punctuality, particularly with long distance services, has been not particularly outstanding inn the last few years.
Incidentally, the local & regional services are put out to tender in a basically similar way to the UK; DB bid in competition with others, and there's an enormous number of private operators. DB only really has a monopoly of inter-city services (there are one or two open access operators, but they're hardly worth bothering about).
The system is
not like the UK. The contracted operators cannot set fares, they aren't responsible for stations, they are fully integrated with DB services and other public transport and they are contracted by a regional authority (as opposed to a DfT-type agency). It's not unusual to see an operator with just one route. The UK uses Net Tendering. Please don't think I am being fussy, there is quite a big difference in terms of what the passenger sees (fully integrated fares e.t.c).
Yes, DB's punctuality has slipped. However, a long-distance train is considered as being late by more stringent criteria than the UK. Connections are often held, which can have a positive and negative effect on journeys and punctuality records.
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DB are not exactly popular in Germany, have they uncrocked the ICE-Ts yet? And the less said about the Berlin S-Bahn debacale (Bombardier Build Quality

)
Are most TOCs popular here? People will always criticize, one look at the twitter feeds to UK TOCs says it all. The press give rail an even worse image. If you took all that at face value, what would you think?
The best thing about DB over the UK TOCs is the ticketing if you ask me. It's FAR more sensible than the UK. To be able to purchase a one year whole-country pass (with virtually no restrictions) for around 3,800 euros is a very good offer. The ticketing is the problem in the UK, it's fragmented and confusing to travellers without a lot of ticketing knowledge. If you're not super savvy on some journeys, you will get ripped off.
Another thing is the unequal distribution of new stock. When I visit relatives living in the state of NRW, most local services have new Bombarider TALENTs, Stadtler FLIRTs or consist of push-pull double decker stock. Even the older push-pull regional stock, makes Northern's Pacers on busy commuter routes look ridiculous! It just feels as if there is much more capacity available to cope with demand.
In short, no it's not a perfect system by any means. However, from an enthusiast and short-distance commuter point of view (I have been one over there briefly), I'd take the German system, at least in the Hannover area. It's the ETHOS of the system, which feels more passenger orientated rather than profit driven.