As a general matter I typically find National to be cost-competitive, if not generally cheaper, but of course it depends on the market you're pricing out and the times (you don't specify where you are trying to rent). Kevin's suggestion is spot on, for weekend rates always start with the LMS rates published each Tuesday.

Taking your premise as true, however, the question is whether the extra cost is worthwhile. Rent with priceline or hotwire and you won't earn any status points, you have no control over the agency you get sent to, you won't get any upgrades, etc.

Of course it's a matter of cost differential, but I'll typically pay a slightly higher rate to take advantage of choosing my own car, almost always getting an upgrade, knowing I'll be getting a pretty new (and key for me, smoke-free) car, earning free day credits, participating in promotions (i.e. 1-2-Free), and earning status.