Just came back and was impressed with Delta Club. Wow, one of the best lounges I have been into. Spacious, not busy on Sunday AM. Breakfast was great with eggs, lots of choices for kids. My only complaint was one espresso machine. I wish I stayed for lunch as they usually have Ivars Clam Chowder and Beechers Mac and Cheese.
Went to peak at Amex Plat lounge also. Like everyone said in previous posts, much smaller, people hanging out at every nook and cranny and only 2 bathrooms that were single stalls. Food was also not as good as Delta. It looked gourmet but tasted average. I was there for lunch spread and it was chicken banh mi sandwiches which were not half bad. The flatbread veggie sandwiches were tasteless and desserts were some sort of crumble squares that was not appetizing. The salad bar looked good but wasn't into a salad at that time.
One option for Amex plat is to add additional card holders with passengers name on it to avoid $30 fee but each additonal card holder costs extra ($175) for 3. I have Amex Plat Ameriprise so it is free if you have that card. But the Delta Skyclub beats the Amex Plat lounge out of the water. If you are staying a long time in Seattle it may be worth it to pay the extra to stay there. You could just pop into Amex Plat lounge to see how busy it is before making your decision. And check out the Delta lounge to see if worth $30 per person to you. They are both right around corner from each other. Also check out the Sub Pop store in Central terminal if you like seattle grunge scene. Really great store that brings back memories of my youth