I would say that, unless you have a contract with either client which contains a competition clause, then you are not legally obliged. Lots of designers and illustrators will work for firms that are in competition - e.g. magazines, publishers - so I would think that a client would need to specifically request that you don't work for other firms in competition with them. This would be quite unusual, because it represents a restriction of your trade, and there are laws against that. It's different where you're working for a company as an employee (not freelance), where contracts often stipulate that you should not work for other companies in competition against the employer. But this would be quite unusual in freelancing, I think.
If you think either company might be upset, then that's a different issue. You might want to keep on friendly terms for further work, so you might consider broaching it. But really, a client should take it as understood that a freelancer will take whatever work they want.
Those are just my opinions, based on experience and common sense, so please take with a pinch of salt! Check any signed agreements that you have.
