Ankarsrum Watts

My guess would be because Europe is 220v and we’re 110v. 

That wil be the only difference I guess. 

Watts rating is more or less meaningless - it is peak power consumption, and has nothing to do with power it generates or torque.

Ankarsrum, the Swedish company that manufactures the Assistent, is a sister company of Ankarsrum motors--literally, too, as its factory is on the same site.

From the manufacturers website:  

Why does the US Assistent have 600watt and the European 1500watt?

The reason for the wattage difference is because of the different voltages used in Europe and the USA. However the strength of the machine is no different

5/21/2020: this statement has bugged me since I first read it.  It does not directly answer the question about what is the (actual) physical difference between the two models and their motors.  

As Suave notes, rated wattage (usage) is not an absolute indication of power.  An inefficient motor (or product) can have a high wattage and low mechanical power, i.e. a lot of the electricity it uses is converted to heat.  It is analogous to the difference between an incandescent light bulb and an LED--both can put out the same amount of light, but the former uses a lot more electricity (watts) to do it.  I don't think that is the case here.

Ankarsrum is a smart company and this is basic engineering for them.  The 1500 watt motor must be more powerful (as in hp or mechanical power) than the 600 (or 800) watt motor.  They are not going to put a less efficient motor in a newer model and then advertise it as better or the same as its half-rated predecessor.

Ankarsrum could make one mixer with two motor options: 110/120v for North America and 220/240v for the rest of the world.  The wiring was spec'd for North America since the lower voltage motor would draw higher current for the same wattage rating (450, 600, 800).  When the marketing department came along and asked for a mixer that would out-compete (out advertise) the competition, i.e. more power, more watts, the engineering department said "no problem" and gave them a 1500 watt motor which at 220/240v would have almost double the power (at the same efficiency) and draw about the same current as the 800w mixer in North America (likely with no other or minor modifications); the Assistent was overbuilt from the start.  It would have been a technical no brainer.

However, doing so would create a marketing problem when the North American market realized the difference.  They would have two choices: make an uprated version for North America (at higher cost) or spin their advertising.  They've obviously done the latter.

But does it really matter?  Probably not.  There is absolute power and then there is fitness for purpose.  The Assistent mixer has had an excellent design from the beginning.  I have a 450w N24 and it can ably handle a full bowl of 65% hydration dough.  Yes, it lets me know it's working, but I've never felt a need to upgrade.  A comparable amount of lower hydration dough, i.e. pizza) might challenge it some, but one could easily just split it and mix in two batches.  Extra power might be nice for grinding meat or flour--but I suspect not absolutely necessary for the scale of a home cook.

1500 watts looks good for advertising, but as any Assistent owner likely will tell you, it's overkill.  Same way a 300+ hp car is overkill for most drivers; we have been trained to want it, but don't need it.