I have two which I can compare:
1) HD 25 Adidas (= same sound, crazy colourway (which kinda suits the way they sound)) - bright, superb PRaT, light, durable, replaceable parts, easy fit, great isolation, unwieldy (effectively take up as much space as T5P or Ed. 8). Amazing for gym, and once in a while I pick them over Edition 8 for their PRaT (and don't forget the colour!). Nice synergy with Shuffle (2nd gen.), Sansa Fuze, Sansa Clip+, fine with Tera Player, too.
2) DT 1350 - subjectively seem to be more accurate, clearly better for classical and for analytical listening in general. Heavier but still OK, fitting takes practice, but once mastered, isolation is great, very good travel case, - my missions/ travel solution. Do not go well with Shuffle, very good with Fuze, Clip+ almost the same, little used with Tera Player (it was a fine match, but others were better).
For me Edition 8 [when used with Tera Player] combine the best of both worlds - detail of DT 1350 and fun factor of HD 25 II, with comfort far surpassing any of those two; however, for classical and jazz T5P beat them all (well, it's not like day and night , but once you hear the difference, it grows on you...).
I'd say it would depend on musical taste and future plans (any [particular] more expensive cans envisaged), but both HD 25 II and DT 1350 are sound choices.
I have no opinion on P5: my salary is paid by EU taxpayers, therefore it seems just a question of common decency to spend it on locally manufactured items whenever I have the choice (= hence also Tera Player ;-))