"Can" can mean either "to be able" or "be permitted to", depending on the context. If I want to avoid any confusion as to meaning, I would use "able to", as you sentence: I´m feeling much better now, so I am able to go out.". "Can you drive now?" could either mean "Are you able to drive?" or "Are you permitted to drive?" The form "could" is also used to make a polite request: "Could you please see me after class?"

The problem in your example is not one between "could" and "was able to". The problem is in the cause-effect relationship created by "so". Technically, there is nothing wrong with the "could" in: "I felt better on Sunday, so I could go out." The problem is with the clarity of the cause and effect, since the word "so" can mean "and so it resulted that" or it can mean "for the purpose of" / "in order that". Therefore, your sentence is ambiguous (can be understood three ways): 1.) "I [forced myself to feel] better Sunday, BECAUSE I WANTED TO go out (and I did go out)." -or- 2.) "I felt better on Sunday, and THAT RESULTED IN MY ABILITY to go out (and I did go out)." -or- 3.) "I felt better on Sunday, and THAT RESULTED IN MY ABILITY to have gone out (but I did not go out, even though I was well)." 2.) "I felt better on Sunday, so I was able to go out" leaves less room for confusion, so it is the preferred choice for what you meant. By the way, the other meanings could have been clarified this way: 1.) "I made myself feel better Sunday, so that I could go out." 3.) "I felt better Sunday, so I could have gone out."

generally there is a very small difference between them. CAN = ability / strength + permission. e.g; Can I speak Chinese in the class? No, You can't.[This shows permission]. But, I can speak English very well. [this shows ability]. On the other hand 'be able to' as the word 'able' suggests shows only and only ability. Ex.,I will be able to speak fluent English one day.[The last sentence is especially on behalf of you. Best of Luck]