My understanding is that Science tend to accept biological papers investigating fundamental mechanisms. We have a manuscript which is about a novel computation software suite for drug discovery with very good results applied to both animal and human data. The consensus is on going for Nat Biotech but I was wondering if Science would accept our manuscript.

This really depends on the focus of the paper. Is it on the biological conclusions? If so, Science may very well send it for review. If it's based around the tool itself and the validation/biology is secondary, I'd be very surprised if Science accepted it or even sent it for review. Papers like that are more typical in Genome Biology, Nucleic Acids Research, Bioinformatics, etc. Which are still major journals for tool development papers and by no means a poor target.

Also, do you think if a manuscript gets scope-rejection in one of the major journals, then it has lower chance for being accepted in another major journal? Like journals may share their information about submitted papers.

Generally, no. Journals are in competition to a degree. Families of journals may share certain info, but this is typically only the case when it's directly transferred (with your approval) between them within their internal system.

Science is a general journal that accepts all kinds of papers, though it does lean toward biological papers in terms of overall number. Its readership is general, which includes computational work. However, the emphasis is on the novelty and generality of discovery rather than the novelty of tools. Sure, it will count for something if you have found something novel using a novel tool, but the novelty of results trumps the novelty of tools.

Take, for example, a classic Hinton paper about dimensionality reduction by neural networks. There is no biology in it whatsoever, but there is a cool new tool (autoencoder). What probably pushed it through is the fact that it was applicable to all kinds of data, so novelty of tools + novelty of results + generality = Science paper.

Nature and Science are competitors and will not share any data about submitted papers. However, there may be some sharing within Nature and Science families of journals. Separately, being rejected by one major journal may mean that your chances are lower in another major journal, but not for reasons of data sharing. It has to do with similar publication criteria of major journals, so if it isn't good enough for one of them it likely will not be for the other either. This is especially true for manuscripts that get rejected without reviews, because that indicates incompatibility in terms of publication topic rather than scientific merit. Major journals are aligned similarly when it comes to their topical interests.