You asked about doppler, but getting mixed into the discussion is broadband vs pulse, along with small antenna/wide beam vs large antenna/narrow beam. Each affects performance in different ways, and of course they all inter-relate in various ways.
I think you can only do doppler with broadband, so they go hand in hand. And I'm pretty sure Furuno is the only company using doppler to assess movement and color targets according to danger level. To me this is a very useful feature derived from broadband, and highly applicable in the consumer market where people are not trained on radar operation and understandably need/want simple operation.
The other feature Furuno has recently introduced is their target analyzer. This is available in the NXT broadband radar, and also in their new dedicated pulse radars. It constantly analyzes all targets so when you click on one for ARPA, it comes up right away (or at least much faster than traditional ARPA). This too seems like a really useful feature, but note that it does not depend on broadband to do it.
If you bought a NXT radar you would get both of these capabilities, and personally I find that very compelling.
But, there are a few potential down sides to broadband that are typically swept under the rug. I say "potential" because I think, with varying levels of success, vendors do tricks to work around these inherent problems. But if I were evaluating the NXT radar, I would want to understand how these issues are handled. They are:
1) RACONs. Major buoys are often equipped with RACON and will return a strong, identifiable return. Broadband radars typically don't trigger RACON, so this navigation tool is rendered ineffective.
2) Interference from pulse radars. I found this to be a really serious issue with the Simrad 4G. When you get swept by a bigger pulse radar, it creates interference spikes radiating from your boat on your radar screen.
This article shows an example screen shot of a mild case. The worst I encountered was a crossing ferry, and as the ferry got closer, my radar became increasingly unusable due to the interference. This is one of those dangerously escalating problems where the closer a boat comes the more you need your radar to track it, yet the more unusable the radar becomes. In engineering and math this is known as a positive feedback loop. The Tacoma Narrows bridge is a well know example of a positive feedback loop.
Anyway, I expect over time vendors will get better and better at working around these inherent broadband issues, but if I were considering the NXT radar, I'd want to hear Furuno's position on this, or better yet, find people using it and see what they say. My policy still holds that if a vendors lips are moving, they are spinning a story in their favor. The less charitable version is that they are lying.
A lot of people know that I've been very critical of Simrad's radars (pulse and broadband alike), but in all fairness I can't say that broadband technology is inherently good or bad or better or worse than pulse. It's what you do with it that counts. It has some inherent pluses and minuses, and everyone will have to decide what matters to them, hopefully based on factual info rather than repeated miss-information. But broadband or not, I think Furuno has some really useful new features, including at least one that is only possible with broadband and dopper.
Oh, and back in your original question you wondered about a 4KW dome vs NXT vs a larger open array. I think for typical trawler cruising a 4kw dome is just fine and will give you 90% of what a larger open array will do. So unless that extra 10% matters, I'd save the money and stick with a dome, either 4kw pulse or NXT.