While I expect spiral cutter heads are a better choice, they are not in the budget for one piece for a customer. With the traditional 3 knife cutter head in my 8" PM jointer and I think 2 knife head in my 15" Jet planer, how likely are some of the eyes to pull out when surfacing birds eye maple?
That depends on a number of things, sharpness being the most important since you won't have control of some of the others like sharpness angle and cutting angle.
Another thing that helps reduce the risk, is to wet the surface right before running it over or through the machines. Wet wood is only about half as hard as dry, so it makes it easier on the knives. However let me warn you to be sure to wax your jointer beds before you try to surface any wet wood. The wetness makes it try to stick so feeding it becomes jerky. That won't be an issue with the thickness planer.
I used a combination of the previous replies with good results before changing over to a Shelix head on my 8" jointer.
If I had to dress figured wood for an important project I would remove and sharpen the knives on my jointer head using my Tormek. Then I would joint the material using a very shallow setting and slow feet rate. Once ready for the planer (13" two-speed Delta lunchbox) I would dampen the surface with a wet sponge and feed at an angle when I could. Even if there were rough spots from the jointer, they were usually improved by the planer due to the higher speed of the cutter head.