There are several ways of knowing how the enemy is equipping ships:
1. As stated, check in the diplo screen; look at the latest, largest warship the opponent of choice has.
2. Once you've got some level of intelligence, you can directly click on enemy fleets and see their stats.
3. The best way of all, though, is to determine what 'tech your enemies use. either develop one line yourself and trade it to everyone, or wait 'till someone starts down a line, buy it at any price, and then trade it to everyone else. The develop a different line yourself -- you may need to research periodically in the 'bait' line to keep some of the more agressive AIs on-track -- and develop defenses to the line you're feeding everyone else.