Avis Preferred First will match you into the Executive tier at National...maybe try and achieve that status with Avis before making the jump?
https://statusmatch.emeraldclub.com/ Just an idea. I don't know the Avis Preferred terms, but maybe try and reach the minimum number of rentals to get the status using points/free coupons/cheap weekend rates before jumping ship completely.
Short answer, absolutely worth it. If you like getting to choose your own car (my favorite part of the program) and driving mildly interesting vehicles for a mid-size price, switch. I think most of the National regulars would agree.