Do they have modern interior?
Most of the departments aren't older then Victorian era at most (mainly a few on Downing Site), and all have been refitted with modern amenities. In fact the majority of departments are modem buildings put up in the last 20 years or so - most of the buildings on the West Sites have only come up in the last few years! The university is in a constant state of having new buildings erected and old ones demolished. There is a sense that the university puts up a new building having already planned when they will be demolishing it and replacing it 10 years hence...
I don't know about Oxford - Oxford Mum or nexttime may be able to comment on that side of things more. For Cambridge though the buildings that "feel" the oldest inside are mainly the holdovers that went up in like the 80s or 90s and haven't been upgraded since (like the one I work in...). The ones that look old in terms of architectural style usually have the best modern amenities inside and the old architecture and interior design is just preserved for the aesthetic facade, as typically they're major listed buildings which the university makes sure are very well maintained and fit for purpose (e.g. the Old Schools and Senate House).
My third year room was fairly cold as the old stonework and windows were hard to insulate in any way, had to use the heating a lot. That was about the only downside. Lots of tourists would fly thousands of miles to see where I lived. Twas weird.
For the younger son (Oriel) it was a completely different kettle of fish. His first year was spent in the Rhodes quad, looking out onto the High. The room was massive, with an original feature kept in - the 1911 fireplace, and very beautiful it was too. The mullioned windows too, made it feel very "Oxford". It even had a little ensuite bathroom. However here the similarities stopped. It was filled with an awful hotchpotch of styles and the furniture was very basic and looked a little shrunken amidst the massive room. I had fantasies about winning the lottery and re-furnishing the room in olde worlde style.
With the second year room, he hit the style jackpot. He went to a set on the top floor, right near the turret of the ancient first quad. The drawback was the steep climb of what seemed like many flights of stairs, and to get to the shared shower room you have to go all the way down to the bottom of the staircase. However the room itself - what a reward! It was straight out of Chariots of Fire. There are the mullioned windows, with great views both of the street and first quad (you could look out from his desk to boat burning and post graduation gatherings), tiny bedroom with 1920s wardrobe and original whitewashed walls and black oak beams, wood pannelled lounge with olde worlde feel and three settees. The settees were from the 80s and bright pink, so the two male occupants had to buy throws to camoflague their Barbie-ness.
So overall, you may like the old colleges' rooms themselves, but don't expect posh antique furniture. The interiors aren't as impressive as the exteriors, and I often think that visitors see the most picturesque bits of the colleges.