Just looking at the grass, I don't think it's a thatch problem (though de-thatching once in a while couldn't hurt; you don't need a thatch rake, just run a metal-tined leaf rake over it and you'll get any dead stuff). It looks like a greenup problem.
As mentioned in other answers, the species of grass you have planted affects when it turns green. Bermuda and other perennial "southern lawn" grasses are heat and drought-tolerant, but aren't as green or as pleasant to walk on barefoot as annuals, and they can have a delayed greenup in cooler climates.
Weed & feed is generally a good thing to do at least once a season, but understand that even though the herbicides used are designed to be selective (targeting broadleaf plants - weeds - while leaving the grass alone), they are still poisons and do still have an effect on your grass (think of it like chemotherapy; the chemo is designed to target cancerous cells but does a fair amount of collateral damage). While the grass is recovering (this can take up to a month), its growth and greenup will be reduced, and germination of any new seeds (good and bad) will be prevented. So, it's generally best to apply weed & feed either as early as possible after the snows have melted and the ground thawed, or more toward mid-season after the grass has greened up well. If you don't weed and feed early, fertilize early; a fertilizer-only product such as Scott's Turf Builder can be applied four or five times a year, and up to a point, the more you fertilize the quicker your lawn will green up and the thicker it will grow. Of course it's possible to "burn" a lawn by over-fertilizing (either too much or too often) so be reasonable.
What you are most likely seeing with regards to the strip of green next to your neighbor's lawn is a combination of a different species of grass, regular overseeding, and better fertilization. Your neighbor is most likely using a scatter spreader, and so whatever he puts on his lawn (seed, fertilizer) will carry over onto yours. No big deal, except you're not doing the same thing he's doing, with the same products, so the difference is noticeable. I'd talk to your neighbor, find out what products he's using, how much and when; it seems to be working for him, so you could take away some pointers.