Operating system. If you have an iOS phone (iPhone) you will find the iPad to be very easy to use. Likewise if your phone is Android based you will find an Android Tablet to be very similar. Other systems comprise such a small percentage of the market they carry a risk of going out of business. I'm sure Microsoft will be around. Right now their system is selling so poorly that you may see them go through several changes. Searching for the magic needed to sell more phones, and tablets.
1. Aspect ratio. To me I like it to be like a standard book page or piece of printer paper. I don't really like the narrow size as much. However they are easier to carry. Especially in a purse.
2. Cameras front and back. If you want to take pictures or video conference you need these.
3. Access to the Google Play store. Without it you will have to get your apps from Amazon or one of the lesser known app warehouses. None are as good as Google but you can get by. Not an issue with iPads.
4. Price. Less is better.
5. Battery life. Most last a few hours and that's fine with me. Consider this if you do not have good habits about charging your equipment.
6. Keyboard. There are some that come with a keyboard like the ASUS Transformer. Most can connect to a bluetooth after market keyboard.
Let me know if I missed something. :-)