I own both: a Kobo Aura One and a Kindle Voyage. I love both, and hate both for different reasons.
Kobo:

• Love the larger screen and the evening color shift. Love the option of seeing my book cover when sleeping or powered down, and knowing where I am in a book (79% complete).
• Hate the laggy software - it's clearly slower than the Kindle software

Kindle:

• Love the snappy, well-designed software, and the ability to sample most books before buying. The smaller size fits a bit easier in my bag. If you are an Amazon Prime member, you can borrow many books for free.
• Hate the lack of color shift, the extra steps needed to convert my Amazon books, and the ongoing effort to lock me in to their system.

Both readers are lightweight, and I have no trouble holding either with one hand (and I have smaller hands). I read over 100 books per year and tend to swtich back and forth between readers as the mood strikes.
These days I buy most of my books through Kobo, and convert them to read on the Kindle using Calibre. Exceptions are Amazon-only authors, and freebies/promotions.