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just my two cents worth - the dutch model of (largely) separate infrastructure is not helpful for longer distances, or in my opinion, getting anywhere relatively quickly on a road or fixed bike. The cycle lanes are very bumpy ( brickwork laid over sand in most cases) designed for slow speed pottering on leafy back roads, all good if you're a leisure cyclist or simply popping to the shops, but for long distance commuting in a major city very unsuitable.

This is certainly my experience from Germany. The long-distance tracks that the Dutch have been constructing between towns are said to be a better surface quality, however.

When cycling in Holland anywhere outside of a town center I used the roads as much as possible, even though it is not allowed, because the cycle lanes were so unsuitable.

I suspect I'd do the same, although some friends of mine were ordered off the road by the police and buzzed dangerously by drivers elsewhere despite the absence of any cycle tracks nearby.

Remember their largest city has a population the same as leeds

According to Wikipedia, the metropolitan population of Amsterdam is 2,158,592. The 2008 population estimate for Leeds (could be census-based for all I know, but any exact population data for this country is hard to come by) is 770,800. It is significantly smaller than Amsterdam. You may have counted only the inner-city population of Amsterdam, which is indeed similar to the population of Leeds, but you have to consider the whole conurbation, not the way in which administrative convention slices it up.

is very dense (as is all of holland)

Don't confuse average population density with actual population distribution. Like all countries apart from city-states, the Netherlands have urban and rural areas. They have some dense cities, but then, every European country does. What people typically try to express when they talk about population density is that the Netherlands are comparatively well-planned, i.e. the distribution of centres there is relatively even compared to other countries (although even in the Netherlands this obviously varies from area to area). This has the greatest effect on transport patterns.

That said, the Netherlands are the most densely populated country in Europe. This has certainly provided a historical imperative for the style of development that they have chosen. It is unclear whether average population density measured across any size of an area has a marked effect on transport patterns, as what really counts for those is the distribution of possible origins and destinations of trips, and the relations between these, not the density. I am not aware of any consistent correlation between density and length of trips or mode of transport used, across different cities. They all have their own characteristics and there are extremely interesting differences.