Just my opinion but ................
The 'service tools' that come with any bike are pretty rubbish quality and you should not really rely on them for anything other than emergencies.
When considering what tools you should carry you should also consider what types of jobs you are likely to need to be doing on the roadside or indeed what knowledge you have to carry out a repair in these conditions - which in reality is not much!
A good toolkit, if you plan to work on the bike yourself, is however essential so get the best you can and just carry an adjustable spanner and a screwdriver when out riding - I always carry a tyre inflator / repair as well. Providing you maintain your bike you are unlikely to need much more.