You can appeal your property taxes to then current market value if the market is lower than the price you paid.
However your neighbor who bought at the very low is capped at purchase price + 2% compounded annually.
Say the neighbor buys in 2012 for $350k. If you appeal, you can have your house reassessed to $350k that year. If the following year, in 2013, prices move higher to $400k (still below your purchase price of $550k), the county can assess you based on $400k. You neighbor, however will be capped at $350k + 2%, or $357k. Your taxes will be $4800 ($400k @ 1.2%) and your neighbor’s taxes will be $4284 ($357k @ 1.2%). The difference of $516 is an air-ticket to Europe in the winter and the market hasn’t even recovered to your purchase price yet — you’re still upside down by $150k.