"unnecessary" means "not needed", sometimes with a hint of "and not wanted"
"not necessary" means "not required"
Some Examples:
"Eating every day is not necessary" - Factual. You can still survive if you don't.
"Eating every day is unnecessary" - This would sound strange, since while it is not necessary, it is normal to do so.
"Rotating your car tires every week is not necessary" - Doesn't really hurt to do it but it's not needed.
"Rotating your car tires every week is unnecessary" - You really don't need to do this.
Additionally:
Oftentimes, there are differences, of varying magnitudes, in meaning between "unnecessary" and "not necessary". In some of these instances "unnecessary" can have a 'negative' undertone. For instance in "It was unnecessary." vs "It was not necessary." , "unnecessary" sounds slightly negative (in the sense that not only was it not required but it was also not wanted).
In other instances the difference is so slight that it might only be regional or not immediately distinguishable. In such cases it might be preferable to use other constructions over take the risk of the nuance being missed.
In other cases, such as "he can remember a lot of unnecessary details" / "he can remember a lot of not necessary details" only one version fits (due to reasons not necessarily related).
Best Answer
"Unforgettable" is a much stronger word. "Memorable" is a much safer word which would normally be selected in a polite thank-you note. Certainly there are cases where the stronger word is also approriate in polite thank-you notes, but the problem is that you don't want to seem to be using overstatement, which can make you appear insincere.
"Unforgettable" means something that is so memorable that it can never be forgotten. Cases where "unforgettable" might be perfectly appropriate include: the weekend at Windsor Castle hanging out with the royal family that the Queen of England recently invited you to, your wedding (for which you want to thank your parents for paying the tab), or the night your band opened for the Red Hot Chile Peppers.
"Memorable" means something worth remembering. It can be used safely for any happy experience. I would use "memorable". By not overreaching in your compliments you will tend to convey more sincerity and produce an ultimately more heart-felt and, thus, powerful thank-you note.