I think there are some quite major differences between Germany and the UK at Christmas. We live in Germany but celebrate UK-style, so I only have a hazy idea of some German traditions.
Main celebration is on evening of 24th, when the prezzies are given out. Families often go to a church service/nativity play on Christmas Eve at around 3pm. 25th is a public holiday, but it's mainly a 'hanging out' kind of day. Although I think the 25th is when people have their 'big family meal', which is mostly goose (but turkey is also known).
On Christmas Eve some families eat sausage (because it's quick and easy), but I think carp (yuk) is also traditional. You're supposed to store it in the bathtub. No comment on whether people really still do that.
Christmas is more self-consciously traditional and old fashioned. It's entirely possible that the family will have a communal singing session of Christmas songs (most of which are very different to British ones) and children might be expected to play their musical instrument or recite a poem.
Most trees are real, artificial trees are not unknown, but certainly frowned upon. Traditionally, the tree would have - eek, wait for it - real candles, and I know families who still do this, but the majority would have electric ones. Christmas decorations are traditionally made of painted wood and are quite low-key but beautifully made. You can buy baubles, but people often find the wooden ones (the best are made by a company called Käthe Wohlfahrt) more authentic. I'm not sure the Germans would be overly impressed by British tree decorations by comparison.
There's also general bemusement at the British liking for sweet fruity stuff at Christmas. Christmas pudding (which they insist on calling plum pudding, must be taught at school) and mince pies are known, but I've managed to convince very few Germans that they're yummy. Their loss! So be careful if you bring one over - it might not go down too well. Also, if you're in a big city, there will probably be an expat shop selling mince pies etc anyway. I bought mine last week.
Crackers (Knallbonbons) are known about, but they are usually smaller and used only at New Year, not Christmas. From bitter experience I can tell you that you are not allowed to bring crackers on a plane (actually you'd better check about that - might be you can't bring them in hand luggage only). We buy ours in Germany from the expat shop, and they've been imported by sea. Shortbread might go down well, but our local supermarket sells Walkers shortbread so it's nothing overly special.
What might be really appreciated is, depending on their tastes, either A. some quintessentially British teas (breakfast tea, ie normal tea, Earl Grey etc) and a bone china teapot. Honestly! Or B. If they're a bit more hardcore, a decent bottle of single malt whisky would be appreciated. Make it really obscure and play up how special it is (only X bottles produced a year, X years old in oak casks, really difficult to get hold of etc) Best to buy one at the airport as you can't bring it in hand luggage and I'd be wary of sticking it in my case because of the danger of breaking.