I may be in the minority here, but my answer to the question in the OP would be: it didn't.
I thought the TMP "fireworks" warp effect was ridiculous. Completely over the top and cartoonish. The TWOK-TUC warp effect and the TNG-era "strech-jump" were both huge improvements (one moment that I thought was really cool was at the very end of GEN, when the three Starfleet rescue ships all warp out together. Seeing multiple ships go to warp almost simultaneously was something we hadn't really seen before in TNG.)
As for the Trek XI effect, I really like it as well. It may be the best one yet. As BillJ pointed out, it gave the jump to warp a real sense of power, an impact, that it didn't have before. The presence of sound effects in space is a long-standing tradition in Trek and other space operas, despite how unrealistic it is, and JJ's movie takes full advantage of that conceit with this great pop sound right when the ship zips off the screen.
Generally, I think the relative simplicity of later warp effects represents an improvement, not a downgrade, over the light-show in TMP.
I thought the TMP "fireworks" warp effect was ridiculous. Completely over the top and cartoonish. The TWOK-TUC warp effect and the TNG-era "strech-jump" were both huge improvements (one moment that I thought was really cool was at the very end of GEN, when the three Starfleet rescue ships all warp out together. Seeing multiple ships go to warp almost simultaneously was something we hadn't really seen before in TNG.)
As for the Trek XI effect, I really like it as well. It may be the best one yet. As BillJ pointed out, it gave the jump to warp a real sense of power, an impact, that it didn't have before. The presence of sound effects in space is a long-standing tradition in Trek and other space operas, despite how unrealistic it is, and JJ's movie takes full advantage of that conceit with this great pop sound right when the ship zips off the screen.
Generally, I think the relative simplicity of later warp effects represents an improvement, not a downgrade, over the light-show in TMP.