I have a question I want to ask on Skeptics.SE and Politics.SE. I can't tell which board is more appropriate. It seems like a toss-up, but I might get better answers overall by asking the question on both boards. Is this discouraged?
Yes, crossposting is discouraged on the stackexchange network. For a detailed explanation why, check out "Is cross-posting a question on multiple Stack Exchange sites permitted if the question is on-topic for each site?" on the general stackexchange meta.
Do you have a fact-checking question and you wonder if it is more appropriate to post on skeptics or politics?
Usually Sekptics.SE does an exemplary job at proving or disproving statements through thorough research. But keep in mind that the notability criteria of Skeptics are quite strict. They expect you to find a claim from a notable source and provide a reference which proves that that source made the claim.
But Politics.SE might still be the more appropriate platform if the fact you want to have checked is political. But note that just because a statement was made by a politician doesn't mean it is a political question. For example:
The President of Elbonia said that Llama flu is a myth and Llama vaccination a conspiracy. Is that correct?
Llama health is not within the area of expertise of a political scientist, so you should rather post this on Skeptics.
The President of Elbonia said that half the world did not ratify the UN convention on Llama vaccination. Is that correct?
This is a question about a political act, so it is on-topic on Politics.SE.