Here's my thoughts on this one, I've owned a Mk5 Golf GT TDI 140 for 1 year / 30K miles which I sold to buy the Civic EX I've now owned for 1 year / 30K miles, so have a good feel for both cars.
Enginewise, the Golf feels quicker, but almost certainly isn't, the Civic is far smoother and more refined. At idle, the Golf is obviously a diesel, the Civic far less so. In the same type of driving use, I found the Golf 3 - 5mpg more effecient on average, based on miles between fill ups, not trip computer readings.
I thought the Golf paintwork poor, and prone to chips. The Civic is worse.
I love the Civic's looks, inside and out. The scratchy dash is a real shame though, I daren't touch it or clean it.
Kit wise, the civic wins hands down. It's also more practical, more spacious, and carries loads better.
Ride and handling, the Golf wins hands down. I also found it more comfortable on longer journeys, maybe just a personal thing though, there's not much wrong with the Civic.
The roadtests I read before buying the Civic said the ride was poor and noisy. Ok, it's not the best in class, but some of the road tests made me wonder if it would feel like being in a cement mixer with a pile of bricks. The reality is, yes it's firm, and thumps over big bumps, but it's a decent overall ride, and nowhere near as bad as some tests make out.
Driving wise, both cars are very similar. I've grown used to the Civic's visibility quirks, and sometimes the rear window is a bonus when it prevents the headlights of cars following from dazzingly you. Controls all feel good on both cars, gear change etc is fine, nothing to choose there. Engines feel punchy on the road, just like a good turbo diesel should. The Golf is more repsonsive, but less refined, so swings and roundabouts.
With the Golf, I visited the dealer twice after buying the car, both times for servicing. Nothing went wrong or fell off, as you would expect from a VW. Servicing costs were more expensive than the Civic, but I have no complaints over the service or dealer at all.
Both cars have creaks and rattles after 30K miles. I'd say there's little in it build quality wise, but the Civic interior is more prone to wear.
My biggest dissapointment with the Civic is the little problems. Flaking laquer on the wheels, inoperable fuel filler, useless bluetooth phone, etc. These are all minor niggles, but they've really spoiled my enjoyment of owning the car. I still love the looks, but after so many trips to the dealer, who never returns calls, never has the parts in stock to fix the problem, and basically appears to just accept all these faults as being the way Civics are, I start to wonder why I sold the Golf...
There's very little between the 2 cars, and if Honda can crack all the teething troubles, and sort out the dealers, they'll be onto a winner. Having owned both for a decent amount of time and miles, I would have to say in my experience, the Golf just edges it as an ownership prospect at the moment.