3 years ago when I bought this comp I was able to play that size. It was ~34_08 that that changed to 10 by 10. Now days I'm limited to 8 by 8. I still have no lag except on season change. My comp is a then cheap ~655$ Asus 4 gig single core with a cheap ~50 dollar graphics card built in. I guess hardware could make a big difference. Most comps are Multi-core. Muti-core comps divide their power between their cores. This game is single threaded so only one of your comps cores can do anything with this game at a time.
Now to make you hate me.
As I type this post I've realized I have 18 tabs open between 3 window. 5 are open on Youtube vids with 2 others open to podcast sites, 2 are open on facebook games, & the rest are in this window, Forums/art sites/everything else. I love this comp & love having no lag with all that going on. & I play DF with all that going on. Normally it's only 12 tabs open.
xD That doesn't make me hate you. The only reason I don't have a stack of videos open right now is my internet would cry uncle, since apparently my ISP employs literal monkeys to be their code monkeys. My computer can handle that level of activity pretty easily. Really, it just makes me think that you like having a decent computer to work on (Unlike, say, my mother who insists on not updating from her steam-powered thing).
What I don't get, though, is how you could run a 16x16 embark. I suppose initially it wouldn't be too bad, but once things get going wouldn't the FPS edge into frames-per-minute territory? I'll admit I've never tried, but still... Late-game antics on a 6x6 scale seem to proceed at a comfortable 20 FPS or so for me. What is the framerate like?