I was only on Santa Cruz for a weekend, and while I was there the city had everything from sunny weather with wind gusts to very cold rain!
Santa Cruz is a much bigger city than Puerto del Rosario, so there were many more pigeons there than I see on my island. I spent a lot of my time commuting, or traveling, between different places, though. So I didn't get to see too much wildlife.
Honestly, the coolest thing I saw was just how green the island is. I was there to run a marathon, so I was able to enjoy the views that included actual plants.
In general, the islands are each unique in terms of climate. Tenerife is cooler than many of the other islands, in part because it gets more rainfall and less of the Saharan winds (especially compared to Fuerteventura).