Clarify Differences Between Games
In Fallout 3 and New Vegas, power armor was abundant, but only in the hands of certain factions. Namely, the Enclave and the Brotherhood of Steel. Once you encountered the Enclave in Fallout 3, you could have easily had dozens of suits of power armor laying around, just like in Fallout 4.
The difference in Fallout 4 is that the power armor is distributed about the wasteland, and not controlled almost solely by these two organizations.
Power armor was utilized by the US army pre-war. So, anywhere the US Army could be found, including the commonwealth, should have had power armor present when the bombs fell. There are plenty of US Army installations in the Commonwealth, and these are often the places where you find the power armor.
After the war, the Brotherhood was formed by remnants of the US Army in California. They began collecting all advanced technology, including power armor. So, right after the war, there should be power armor everywhere that the US Army was, which is all over, but over time that power armor would have been collected and hoarded in any locations where the Brotherhood was active. The Brotherhood only began acting on the east coast in the last few decades prior to Fallout 4, in Washington D.C.
Brotherhood activity has only recently expanded to the Commonwealth. When the Prydwen shows up, common people can be heard asking who the Brotherhood even are. This means that they have not had time to collect pre-war technology in the area, including power armor.
As is pointed out in Fallout 4's loading screen tips, some enterprising Raider leaders have salvaged suits of power armor from the area, which has resulted in the "Raider Power Armor" that you can find in the Commonwealth. In an ideal world, from the Brotherhood's point of view, all of this power armor will eventually be collected by the Brotherhood.
Therefore, I think it's reasonable to conclude that power armor is more freely available in the Commonwealth because the Brotherhood hasn't gathered it all up yet.
Note: Most of the historical information referenced here can be corroborated by articles on the Nukapedia, particularly the Brotherhood of Steel page, especially the "Origins" and "Operations in the East" sections.