On the S10 I've run Michelin Pilot Road 4s and Avon Storm Ultra XMs. On the VStrom before it with the same tyre sizes I ran Anakee 2s, Anakee 3s, Pilot Road 3s, Pilot Road 4s, Dunlop Roadsmart 2s and Continental Road Attack 2s.
I found the Michelin Pilot Road 4s and Dunlop Roadsmart 2s to be the best for riding in the wet. In the dry the Continental Road Attack 2s were the best, but they wore relatively quickly and once worn the wet handling was not as good as the Michelin or Dunlop tyres.
Stay clear of the Avon Storm Ultra XMs, I've grown to hate them and they are due to be replaced on my bike in a couple of weeks.
The Anakees are OK wet and dry, but not as good as the purer road tyres, and more noisy.
Personally, my choice would be between the Pilot Road 4s (dont get the trail version on the rear, I've tried both and there is no apparent difference in grip but the non-trail lasts longer), and the Roadsmart 2s, but if I lived in a warmer climate and rarely saw rain I might go for the Road Attack 2s.