How would you compare and contrast the message about science and integrity in Frankenstein and The Strange Case of Dr. Jekyll and Mr. Hyde?

Dr. Jekyll and Victor Frankenstein have several things in common when it comes to how and why they used science. Let's consider just two of these commonalities and the messages we get from them.
First, both have selfish motivations for their scientific experiments. Dr. Jekyll is trapped by Victorian social conventions and seeks an alternative lifestyle where he can be free and explore his worst ambitions. Frankenstein wants to create a whole new race of man; this will of course (he imagines) lead to fame, but he also imagines that this race of man will adore him. The message behind the selfish use of science by both characters is actually similar: don't do it. Instead of being rewarded, each man actually causes his own downfall.
Second, both men carry out their experiments in secret. By any measure, this is not considered "good" scientific practice. Science should take place with plenty of input from other experts and with lots of practice so that one can learn from mistakes, brainstorm with peers, and try to improve. Because neither man includes others in his process, they both have very little insight into some of the pitfalls they may encounter in the future. As a result, it does not occur to them to try and prevent them. Later, they have no one to turn to when they need help. The message here is that science should not take place within a vacuum: it should be vetted at all stages.
In terms of integrity, each man displayed a shocking lack of integrity when using science both for selfish means and in secret. Both men only considered themselves when creating their scientific experiments, and this resulted in disaster not just for them, but also for many others.

Compare and contrast the messages about science and integrity in Frankenstein and Dr. Jekyll and Mr. Hyde.

I find Dr. Jekyll's use of science to have at least a bit more integrity than Victor Frankenstein's.  Frankenstein dreams of being "blessed" by a race of men which he will have created and "hailed" as something of a hero by them.  He puts science to use in order to achieve personal glory and fame, and because he acts without integrity, behaving selfishly and unethically, he ruins many more lives than just his own.
Dr. Jekyll, on the other hand, doesn't exploit science in order to achieve fame.  In essence, he succumbs to Victorian societal pressure to conform to an incredibly repressive moral code.  His intention is to better himself by making it easier for him to always do the right thing, as defined by his society.  Despite the problems we might find with his rationale (if we take issue with his attempt to rid himself of a fundamental part of being human), his intentions, I would argue, are less self-serving than Frankenstein's.  Jekyll is actually attempting to change himself in order to better fit the (unreasonable) demands of his society, and so his use of science smacks more clearly of integrity than does Frankenstein's.  He shows that it is possible to put science to use in a more ethical way than Shelley's "hero."