The intended niche of the 2 products are very different. The Amazon Tap was in the rumor mills for quite a while, with the promise of having a battery operated, portable version of the Amazon Echo. However, in terms of execution, I thought it was a little disappointing, especially on the portion about having to tap on the microphone symbol before the Amazon Tap wakes up to take commands, like the Amazon Fire TV. The always-on capability of the Amazon Echo was one of its biggest draws, and contributed immensely to the usability and value of the device. Having to press on the microphone button each time just takes away so much of the magic of the original Amazon Echo. If I wanted to bring a set of portable speakers to the beach, I would be bringing a speaker with a much better quality of sound than the Amazon Tap.
The Echo Dot is a really interesting product though. The small form factor makes it a viable addition to every room as an intelligent alarm clock or smart home control point. At half the price of the Amazon Echo, it might also appeal to buyers who are interested in the Alexa functionality, but do not want to spend the full amount on the Echo.
The smartest point about this product is that while it appeals to the lower-end consumer segment, the fact that it has a line out to your external speakers means that it might become more valuable than the original Amazon Echo to the high-end consumer segment. The fact is that while the Amazon Echo's sound quality is good for a small speaker, it is far off from being satisfactory for a typical audiophile with a decent sound system. The magical line out capability of the Echo Dot means that the high-end consumer segment can now add smart Alexa functionality to their existing expensive sound systems.
For that point alone, I'm gonna predict that the Echo Dot will be a roaring success, and I've already made my maximum 2 orders for the Echo Dot. The 2 products are scheduled to be released on 31st March, and after placing my orders today, I'm already back-ordered to be delivered on 11th May. Note that to trigger the Alexa ordering of the item, your 1-click address and settings must be well configured to the correct US address in Amazon.
Will update this post again when the product finally arrives!