Allen was arguably better than Pierce when they joined up, but Pierce was younger and took less of a backseat than Allen, so he built up more stat equity when they were together. They both only had 2 All NBA 3rd Teams before playing together, but Allen is the only one of the two that finished in the top ten in MVP voting. Allen had 7 all star appearances to Pierce's 5. They both had 4 post season appearances making the conference finals one time. That is before they joined up together. Allen was in the league longer and was older, so he was more at the end than Pierce, and Allen was fine taking 3rd fiddle (pierce wouldn't have been). They were both clearly behind Garnett, but were right next to each other. They were all multiple time all stars and all nba team players though. That is why you could call them a big 3. You can't do that with this current team. Smart just isn't in the same class as Brown, let alone Tatum.
Also as an aside, the disrespect that Allen gets on this board is quite shocking. He was a clear HOF and was very much on the same level as Pierce. As further evidence, in 2020 ESPN ranked their top 74 players of all time. They had Pierce at 54 and Allen at 56 (Vince Carter was between them).