It really depends on the herb Dave.

I freeze dill & basil in whole sprigs, wrapped well in both plastic wrap & foil, but also freeze pureed basil & basil pesto in cubes.

I've gotten away from drying my own herbs over the years, just find freezing or buying fresh from the grocers during the non-growing season much better for my cooking.

But that said, I do dry thyme, rosemary, & other Mediterranean herbs that tend to hold their flavor.

First, I dry most of my herbs then freeze them to protect the freshness. I freeze them in double freezer bags.

I raise most of my herbs and this system seems to work just fine for me.

Basically, you'll end up doing it in your own way, depending on which herbs you want to store, and how you use them. Drying is suitable for most herbs (but not chives!), but if you have a lot to do, it can be messy around the house for a while. Freezing will usually give a better flavour - but maybe you have a ginormous freezer and don't want to be hunting around in it for small parcels while in the middle of preparing your dinner, and I don't recommend freezing if you keep your freezer a long way from the kitchen or if you have an unreliable source of electricity (perhaps a lot of blackouts due to storms?).

I'm not so organised that I follow my own advice, but if you decide to freeze your herbs, do each one on a flat tray, then either bag it or put it into a small container. Then put all the herbs together, each packaged separately, into a larger container or a large sealable bag. This will make finding your herbs easier and quicker. For things like chopped parsley or chives, the ice cube method is very convenient - just the right amount for adding to your stews etc - but once they're frozen, bag them or put them into a suitable container. Small packages tend to get lost and forgotten even in a small freezer. (Ask me how I know!)

Don't forget to label each container.

Why not experiment by both freezing and drying your herbs, and see which you tend to reach for first?

Most herbs I dry. The exceptions would be scallions and basil. The flavor is held much better if you freeze those.

You'll have to figure out what works best for you. I don't have a lot of time to spend on this so here's my favorite way to dry curly parsley - every few weeks I snip some, put it on a paper plate and microwave for about 2 minutes. Let it cool and make sure it's dry. Then crumble it & put in a jar. It smells so much better than store-bought dried parley.