It's Tower but with a slightly different policy.

The look-and-feel of the web pages are identical - just the logos (Tower vs Trademe) change.  I had Tower car insurance at one point.  When I changed cars I looked at Tower vs Trademe - same policy conditions but Trademe cheaper so took it.  I changed my other car from Tower to Trademe when renewal came up.  Its is a decision I have never regretted.

The claims process for Trademe is good with timely settlement on both claims so far.  It is easy to use the panelbeater of your choice.  So I would recommend

Also switched to TradeMe when my tower renewal was going to be more expensive, have had to claim Windscreen cover 3 times now, had no questions asked and claims sorted quickly. 

My personal opinion is that Trademe Insurance and Tower Insurance are one and the same. The reason I believe this is because I have one car policy with Trademe and another car policy with Tower.

I called Tower last year to make a claim on my VW and when I gave them my name and ID information, they said "Ok so you are calling about your Ford Focus?". I had to point out that my Focus was not insured with Tower and they were like "oh yea, sorry about that". The phone agent couldn't possibly have known I owned a Focus unless they could see both policies listed on the screen in front of them.

Having said that, when I was shopping around for quotes, the VW was cheaper to insure with Tower, but the Focus was cheaper to insure with Trademe. So whatever algorithm they use, Trademe is not always cheaper than Tower, and vice versa.

[EDIT: Just to add that my claim through Tower was handled and resolved quickly and easily, and I used the panelbeater of my choice. I imagine a claim through Trademe would be handled in the exact same manner based on my anecdote above]