Who is...
 

I think Gackt would be it... MAYBE!! :P

SMAP?
or Mr.Children?
idk @_@

^I think they mean solo artist.

In which case I wouldn't really know, although my first guess would maybe be Ken Hirai.

i can't think of any male individuals that mirror Ayu's success, but groups or boybands like Mr.Children & SMAP are good examples.

what about Fukuyama Masaharu? he's a good actor as well as a musician.

Yeah, I mean a male musician, not a group or whatever.

In Asia I would say Rain but for Japan I'm not sure

hmm if only a solo artist~ i'll go with ken..

I used to have access to a list but I can't find it, I don't know about solo artists, but B'z, Mr. Children and Southern All-Stars are the three acts above her on the top selling Japanese artists of all time list, and they're all male groups.

solo male artist...
hmm...maybe
ken hirai or fukuyama masaharu
but solo male artist really weak these days

The prince of Enka hikawa kiyoshi!

In terms of popularity and image, Gackt would probably fit the lot. His sales are definitely a lot lower than Ayu's, but he has a large influence (or had).

Hmm...yes, I would say Gackt too.
Besides sales and influence...they have some similarities, and I can't really think of any other solo male.

1. Both of them are very good looking, have a similar sort of prettiness, and are types that leave a strong impressions.
2. Both of them are dramatic stage performers, though Gackt definitely tends to...move more.
3. They both have uncommon unique types of voices. Of course everyone has a unique voice, but their singing styles are more...recognisable? Ayumi has a very high-pitched voice (used to at least), while Gackt has a pretty low one. Instead of choosing a guy who sings in the higher range, I think it's more interesting to have a contrast? XD Kind of like (extreme?) representation of either sex.
4. Adding on to the previous point, they're kind of like the 'perfect' image for males and females. I mean, there was even this manga that pointed it out. Something like how no one could be as perfect as Ayumi and Gackt? Saw it on a thread a long time ago.
5. Lastly, I think that they both like to have control over matters. I'm not too sure about how Gackt works, but he gives me that impression of a perfectionist, much like Ayu.

And that ends my rant ^^;; Oh, and of course, they're very fashionable =D

Oops, I don't suppose I'm really answering the question.
In terms of music similarity...I think their lyrics for romantic songs. It's very hard to explain, but the details in them hold very deep sincere feelings. And also, the use of words, though a lot of Jpop songs use the same words, Ayu and Gackt's lyrics are more poignant, they're not as...playful. I can't find the right word...

GACKT- has had the same impact on japanese culture from Fashion, Music, Style etc.

KEN HIRAI I don't even need to look at the other answers

ken hirai probably...

although gackt is a little closer on impact i think...ken hirai might be more popular...i don't know...there's not too many male singers i really enjoy.

I would say hyde if it was true lol

I dun really think any male artist can be compared with ayu at all.

1) Mr. Children and B'z are legendary artists and I think they have higher statues than her.

2) The boy bands.. SMAP? I dun really think so. They did have 2 to 3 high selling singles, and they have bigger overall influence than any other boy bands (I refer to those johnny boy bands). Overall I think they're pretty weak in music influence. Their fashion influence is not that big, and they only have the statue of being the highest boy band in Johnny. They can't even compared with B'z or Mr. Children.
(Besides, I think Takuya Kimura was really the main focus in the beginning of SMAP. Right now 5 of them are important because they have been in the industry for so long. I dun really think they're that great as musicians).

3) Ken Hirai. Honestly I dun think he's that popular except during his 9th to 10th years. He can't be compared with ayu at all.

4) Gackt. OK I think in fashion and character influence, he can be compared to ayu. But his music again is not that shiny at all.

5) Fukuyama Masaharu. I think his popularity is pretty consistent throughout his career time line. He's very popular... But again he hasn't reached to a level yet that he can be respected like B'z or Mr. Children or ayu or hikki.. so he's not the best example.

6) KinKi Kids. They do have a consecutive single streak like ayu does. (Most importantly, their streak has begun since their debut single... which is more legendary than ayu's no.1 streak). Hmmn... somehow I dun think they're at the same level as well... Not that they can't be, but... hard to explain.

It's really hard to find someone on par with ayu at this moment. Right now ayu is like a beginner (or intermediate) of being a female legendary artist. I dun really think there's any legendary male artists besides B'z and Mr. Chidren. Ayu can't be compared with those two legends, but then IMO other male artists are not lengendary enough to be compared with ayu.

Between Gackt or Ken Hirai

GACKT! they both seem unreal :P