Rank Vs Linear Correlation; which should i use?

I'm comparing two vectors neither of which are normally distributed due to outliers (i.e. long tails). When I use Pearson's linear correlation I get a very significant p-value (~10^(-25)), yet when I use Spearman's rank correlation I get no significant correlation (p=0.7). Am I correct to trust Spearman since my data is non-parametric? What are the possible reasons for getting such a strong linear correlation?

Thanks in advance.