Dripping: Least mechanical problems (zero wicking issues), best flavor, for me...NO dry hits (once you get good at it). More "work/motion".
Tanks: No need to drip. Sole reason for using them or anything that "holds juice"...cartos too. All have issues feeding juice to the coil sometimes.
Also, atomizers last longer than cartos. So if it's a carto tank...that makes a difference. DIY coil tanks vary...hard to compare in general without specifics.
I dripped for two years strait. Still thinking of going back to it for most things other than driving...then tanks or cartos are better. The main reason I have a tank is to be able to build coils from supplies just in case something happens to the marketplace. Been trying to "get good" at tanks...I do OK, but I don't have the $$$ to buy the latest-tank-of-the-week all the time and frankly, dripping is the best.
You'll hear comments like "I only drip to taste flavors" or "It's too much work!". Bah. It takes some practice but you'll get the hang of it quickly. Use a standard atomizer (with bridge and "innards"...don't shell out extra $$$ at first for some special 'dripping atty') and get a drip tip or just remove the plastic cart, drip, and put it back on. Removing the fluff from the cart and trimming a mm or two off the end is recommended if you're not using a drip tip. Drip 3 drops in it, vape about 10 hits until the vapor flavor gets reduced, drip 3 more drops, etc.
Remember to blow out the primer from a new atty and prime it with about 4 drops of juice the 1st time it's used.
It's not any more work than "ashing" was when you smoked. It's kind of a pain that you have to carry around a separate bottle. I used to use small bottles...like 3 or 5 ml...and it isn't much different than having to carry a lighter, if you think about it.
P.S. Don't forget to blow the atty out twice per day to clear gunk and clean it once in a while. I used to have atomizers last at least a month or two. Many got much more out of them.