Well, the A-1200 is an AGA machine, sure !
A-600 and A-500+ are ECS machines.
ECS particular is only the difference that these Amigas have an ECS graifk chip ( ECS Denise 8373 ).
But since this ECS chip needs a better Agnus chip which can adress at least 1MB of chipram, ECS commonly also stands for an Amiga with the following specs:
1) ECS Denise
2) 1MB chipram
3) Kick 2.0
A-500+ & A-600 have all of these.
I haven't tested it on a A-500+, but only on my OCS A-500, but switching to 1MB chipram and Kick 2.0 didn't help so I guess it either needs more chipram or a ECS Denise.
I will check it on an A-500+ later.