It really is going to depend on what feels better to you.  At least both items are pretty cheep.  I will say personally I prefer the headband.  This is more because I have long hair than anything else.   If I tie up my hair than the cap won't cover my ears.  If I braid it down my back then it mixes with my sweat and irritates my neck and back.  Also I don't like like the hat pushing my headphones into the back of my ear.   I just bought a new headband at Target for $1.98 yesterday.  So if you try it and don't like it.....at least its not like paying over $100 for shoes and never wearing them.

I just delt with this myself. I'm a heavy sweater and used a standard beanie (toboggan, skullcap..etc), Then i tried a sweat band, not bad, just felt like it was going to drop in my face. I ended up with this--> http://www.pearlizumi.com/product.php?mode=view&pc_id=28&product_id=1455257&outlet=.  Works great! Breathable and light weight!

I like it..But, that's just my $.02.

Good luck

I am bald and I run in the wintertime. I would buy both. I've had great luck at T.J. Maxx and Dollar General and Kohl's finding tech fabric gear. You can rock the skully when it's not too bad, and just add the headband when it gets too frosty.

I'm in florida so I used a beanie or Under Armour Hat (it doesn't blow off)