If you are planning on going on a multi-day ride or just riding a long distance in a day, you should have something for first aid, just in case. Unfortunately, almost everyone who cycles frequently will go down at least once in their life. This kit can be really small and compact and can include bandages, some gauze, and a small bottle of a disinfectant.
On the other hand, an on-bike repair kit will be a much smarter selection of tools that you are most likely to need. You should figure out the type of screws that are fitted on your bike and the things that are most likely to go wrong on a ride. Address only these things so as not to burden yourself too much with unnecessary stuff. Moreover, there are bike repair kits used on long rides and those used on shorter rides. The longer the ride, the more tools, and spare parts you will have to bring unless you want to have a very long hike back home.
These guys are awesome. After work, I got to my bike to discover my back tire was completely flat. It had a slow leak, so I was able to pump it up enough to make it to their shop. I got there 10 minutes before closing and they were able to fit me in. They replaced my tube and picked all of the glass shards out of my tire. Awesome customer service and they saved me from having to do this myself in the dark and the cold.