The AMC small block was first introduced in 1966. All six engine sizes (290 304 343 360 390 401) share the same basic block design. The different displacements are achieved by different bore and stroke combinations. All blocks share the same external measurements and thus can be swapped easily. Contrary to a popular myth the AMC V8's were not made by Ford or anyone else. They did make use of some Motorola electrical parts (Alternator, Starter etc) like the Fords, but the engine itself is all AMC.
1966-1969 (290, 343, 390)
The AMC small block was first introduced as a 290 in 1966. The 343 came out in 1967 and the "AMX 390" arrived in 1968. These engine blocks were unchanged until the end of 69. In addition to the largest bore and stroke, the 390 motor also got heavier main bearing support webbing and a forged steel crankshaft and connecting rods. The head used during this time, are the so called rectangle port heads, named after their exhaust port shape. The 290 heads use smaller valves (1.787 intake, 1.406 exhaust) in order to prevent problems with the small bore. The 343 and 390 used the SAME, larger valve head (2.025 intake, 1.625 exhaust). You can swap the large valve heads onto a 290 but will need to notch the top of the cylinder bore to prevent the valves hitting, and will probably need different pistons as well. I don't think it's worth it though, the 290 works better with the smaller valves. The large valves are so close to the cylinder wall (on a 290) that they are shrouded by it and will actually flow LESS than the smaller valves.
1970 and Later (304, 360, 390, 401)
In 1970 all three blocks grew in deck height and the strokes were increased on the 290 and 343. The 290 became the 304, and the 343 became the 360. For some reason, however, the 390 remained a 390 in 1970. It wasn't until 71 that the 390 was stroked to the 401. Like the 390, the 401's crankshaft and connecting rods are forged steel. The other change in 70 was the switch to the dog leg heads (again named after the exhaust port shape). These heads are reported to flow 50% better on the exhaust side than the rectangle port heads and are thus the best for performance. There are two reasons for the flow increase. Firstly the area of the port is larger, due to the dog leg. Secondly the shape of the port floor was changed from a concave to a convex curve. The concave floor tended to bend the exhaust flow upwards which caused turbulence when the flow was forced to go down into the exhaust manifolds. By switching to a convex floor the curvature of the flow starts in the head and proceeds much more smoothly into the exhaust manifold resulting in less turbulence and better flow. As before there were two versions, a small valve one for the 304 and a large valve one for the 360/390/401. Again, like the 290, unless you have an extremely radical 304, you're probably best to stick with the small valve head on the 304. The late model 304 head is a good option for the early 290's but there are a few other things to consider, which are discussed later.
Throughout the lives of the heads there have been some changes made, mostly exact valve sizes, and chamber volumes. In general the 70 and earlier heads have about 51cc chambers and run around 10.2:1 compression. Some of the early (pre 68) heads had 53-54 cc chambers for 9:1, the later heads (71 and up) had about 58cc, which gave 8.0-8.5:1 ratio's when combined with the dished pistons used at the time. Using these late heads with the earlier flat top pistons will result in a compression ratio of about 9.5:1. In addition to chamber and compression ratio's some small changes in valve size were made. For example the exhaust went from 1.625 to 1.68 in the early 70's. These changes in valve size are pretty subtle and most drivers would never notice them. In any event you can get your heads machined to take the larger valves if you want, there's plenty of room to do it. You can even put the 343/360/390/401 valves in the 290/304 heads, although this is a bit risky as the castings are a bit thinner on the small valve heads and you run the risk of cracking a head if you open it up too much.
Rocker Arm Assembly
A minor change was made to the rocker arm assembly in 1973. Earlier heads used a round rocker arm pivot. This allowed the rocker some freedom to rotate. The rotation was limited by the width of the push rod slot. Later rocker arms used a cylindrical pivot. This pivot has a bridge which joins the intake and exhaust together maintaining proper alignment.
You can swap heads around pretty easily between these different engines. The 343 heads swap with the 68/69 390 heads, the 70-390, 360, and 401 heads swap. If you want to swap across the 1970 deck height change, you have to watch two things. The early block used 7/16 head bolts where the later used 1/2, and the center intake manifold bolts were re-located. To swap the late heads to a early engine you need a step dowel to ensure the heads are centered properly and you need to file the center manifold bolt holes to re-align the holes. Note that you can't escape the filing by swapping the late manifold onto the early engine because of the deck height difference. To swap a late model intake onto an early block you need to have the gasket face of the manifold machined down to compensate for the different deck height.