No.
None of the free tools can match the value these 2 provide.
That's exactly why these are paid tools.
The best free tool for SEO without any limits is google itself.
With the advanced search operators & google trends you can take your seo research and analysis to next level.
Then there are some browser extensions like SEOQUAKE, DETAILED etc.
The biggest drawback of using free tools is you need more time to collect & organize data.
Also the amount of data collected will be much less compared to paid tools.
The biggest advantage of using free tools is you get a better understanding of the SEO process as you have more control on the process.