Hmm. Well, a lot of the above is sort of inaccurate or misleading, not your fault, largely due to the media, and some poor explanations from scientists I saw interviewed right after the Sumatra quake.
The Atlantic has plenty of plate boundaries. The main one, the Mid-Atlantic ridge between the Eurasian Plate and the North American Plate, is a spreading ridge where ocean bottom is created. The earthquakes there are relatively small and do not generate tsunamis.
In 1755 Lisbon Portugal was destroyed by a massive earthquake (Magnitude 8.7) and tsunami in the Atlantic that killed 50,000 plus people and changed world history.
It's unclear precisely where it orginated but it's related to the complex boundary of the Eurasian and African plates out in the Atlantic. Records were poor in North America in 1755 but there was a tsunami of some significance in North America from it. That quake or a similar one could happen again.
27 people were killed in Newfoundland in 1929 by an underwater quake that caused an underwater landslide, which then created a tsunami (the landslide also cut the transatlantic cables.) It's possible that landslides could occur on the continental shelf at any time, but fortunately they seem fairly rare.
The main reason the Pacific has so many more tsunami is it's filled with long "Subduction" zones where one plate dives under another. There's only one in the North Atlantic, between the Carribean and the Atlantic. This is still capable of generating tsunamis but it's a shorter zone and doesn't have the massive quakes possible underwater in the Pacific. However there have been very damaging tsunami in the Carribean; Port Royal Jamaica was wiped off the face of the earth by one in the 1700s.
Most tsunami experts believe a collapse of La Palma in the Canaries would cause a local tsunami but NOT one that could cause damage in North America. Unfortunately the media has seized on the couple of scientists that think it can like rabid dogs, and ignored the majority of scientists that disagree.
Thanks for the correction. I knew about the plates spreading in the Atlantic and colliding and sliding under one another in the Pacific. I knew there had been a tsunami in Lisbon in the 1700s, but wasn't clear on the cause. If that same one had affected the East Coast, or Central or South America, wouldn't there be some information about it in history? I don't remember ever hearing about it.