IMHO, tripod will always give you the sharpest possible IQ out of the lens. If you going to use flash with flash extender, tripod will be recommended. Handheld will give you the freedom and fastest reaction. There is no right or wrong way, it's depend on your preference.
For your reference, I just came back on a short birding trip with the Tamron 150-600mm on 6D. Since I'm taking public transport, I decided to bring only a monopod and not to bring my gimbal head and tripod as it's quite bulky. I like the freedom (you can go places where tripod is difficult to setup) of hand holding the lens as you can "take cover" and change shooting angle easily, but sometime I miss my tripod especially when you are trying to point your AF point on a small bird jumping all over the place which is just slightly "larger" than your centre AF point on the viewfinder... even with the IS, sometime I find it difficult holding steady and long enough for the AF to lock on it especially later in the day when you are tired. I use my monopod when in such situation and it does help.
Anyway, I prefer hand holding, so must practice more hand holding technique and may be train my arm muscle... ha ha ha
By the way, if you going the tripod way, go for a gimbal head.
Have a nice day.