Here's a quick comparison of the phones:
HTC EVO 4G LTE Details vs HTC One (2013) Details in Smartphones
The One weighs about 10g heavier than the Evo 4G LTE.
Same screen size.
Higher ppi (pixels per inch) than the Evo LTE. The One has 468ppi compared to the EVO's 312.
I don't think the HTC One has a microSD card slot unlike the EVO LTE.
But, the HTC One comes with 32GB of storage rather than the EVO LTE's 16GB.
The EVO LTE only sports a 1.5GHz dual-core processor whereas the One sports a 1.7Ghz quad-core processor.
The One has 2GB of RAM and the EVO only has 1GB.
Edit: Not to mention that the One has a much better battery life than the EVO.