While lavender and rosemary have similar requirement re: sandy/gravelly limey, well drained soil, lavender is much more drought tolerant than rosemary. You let rosemary dry out and you're done. It won't recover. Droopy lavender will recover in a most satisfying way. Rosemary is drought tolerant in the ground only because it grows extremely long roots in search of water. This means it can get pot bound very easily in a container.
Another important point is that many lavender are winter hardy (I have L. x Grosso, L. hidcote, and L. provence that survived last winter in my zone 6b garden) but the hardiest rosemary variety is still a bit iffy in zone 6. I'll be trying to get R. 'Arp' to survive for the 3rd year. Most are only hardy to zone 7 or 8.
I've heard, though have not tried, that lavender is not very indoor friendly to overwinter. The tender lavenders like the Spanish and the French variety are supposed to do better. Rosemary is tricky too. I managed to overwinter for the first time this past winter (tried 3 times and killed them dead). It needed 1C of water every day in a cool SW facing window sill.
Pineapple Sage doesn't survive the winter in my garden, but I was able to pot one up in the fall and keep it alive indoors in a SE window last winter. It did very well until this spring when all of a sudden, red spider mites were all over it. It's out in the garden now, still in the pot. I really have to plant it in the ground so it can really take off.
Basil is an annual -- wait I think H_alex said his stayed alive until spring -- well anyway, I treat them as an annual. I usually let the last of the flowers go to seed and collect the seeds to grow next year.