There's no real difference. I agree

There is no difference informal or when shown in isolation as in your two examples. but there might be a subtle or distinct different in other situations and contexts. You would be more likely to say "if it's any consolation" when trying to comfort someone who is grieving for instance. And you would be more likely to say "if it makes you feel better". When you offer them a choice between two candy bars (sweets in British English) and you both wanted the same candy bar but your friend made a big deal about not having the fought over candy bar. "here you have if if it makes you feel any better". is how you might react.

They are not the same. For example, an aspirin can make you feel better but it does not have any potential to console you. A sympathetic person can console you. A beautiful sunset can console you , even if it can’t make you feel better.