An excerpt from Friends and Other Strangers: Bob Dylan Examined by Harold Lepidus:
Bob Dylan and Neil Young are friends and mutual admirers. They have appeared on stage together numerous times, and have even referred to each other in their songs.
Thrasher’s Wheat is the premier Neil Young fan site. It’s not just my opinion – Neil Young himself has acknowledged the site, and expressed his appreciation and support for all their dedication and hard work:
“This is the most respected site on the net for this type of activity. Let me take this opportunity to thank you for your interest in what I am doing.” 
Webmaster “Thrasher” had been dealing with the Bob Dylan vs. Neil Young comparisons for years. He discusses the “battle” here:
Bob Dylan and Neil Young: A Fascinating Saga by Thrasher 
The relationship between Bob Dylan and Neil Young is a fascinating saga.
While Dylan is universally acknowledged as the most influential and important 20th-century singer-songwriter performing today, Young is among a very small contingent of contenders for second place. Young’s integrity and credibility place him among a distinguished group of artists to be compared to Dylan.
As a long time Neil Young fan, we’ve never really perceived any rivalry whatsoever between the Bob and Neil fan bases, and find the whole Bob vs. Neil discussions to be a bit tiresome. It seems no matter your preference, both men are living legends and musical geniuses.
Nevertheless, the whole Bob and Neil business can be quite humorous.
Back in 2006, we linked over to a blog post on Top 10 Reasons Why Neil Young is Better Than Bob Dylan. The tongue-in-cheek posting created quite a bit of an uproar generating nearly 100 comments from outraged Dylan fans. So what exactly would any Dylan fan find objectionable??
Top 10 Reasons Why Neil Young is Better Than Bob Dylan: 
1. Better Voice
2. Better Guitar Player
3. Better Good-to-Bad Song Ratio
4. Neil Never Sold His Music To a Commercial
5. Neil Embraces the Younger Generation of Musicians
6. No One Plays Neil Songs Better Than Neil
7. Farm Aid & The Bridge School Benefit Concerts
8. Neil Is More Diverse
9. Neil Never Played With The Dead (Note – Yes he has! – HL)
10. Because I Like to Piss People Off
The Eight Track Mind blog goes on to deconstruct each argument point by point. To say some of the reasoning is provocative would be an understatement.
In “retaliation,” the Dylan community returned fire with both humor and wit to which we waved the flag on Top 10 Reasons Not to Goof Around With Bob Dylan Fans.  For example, Dylan fan Mikey spoofs:
More Top Ten Reasons Dylan is Better:
1. Neil’s tendency to make one-off right wing political statements (e.g. “Let’s Roll”).
2. Neil’s Everybody’s Rockin’.
3. Neil does not regularly tour with Crazy Horse, his best band and he obviously knows this fact.
4. Neil stopped selling “Greendale High” t-shirts on-line.
5. Bob’s influence allowed The Beatles to write and record Rubber Soul.
6. Bob is an American and Neil is Canadian.
7. If there is another CSNY reunion and I have to see Graham Nash on stage, I may off myself.
8. More Star Wars Jawas on stage would have made Live Rust a better video.
9. Neil has never been called Judas.
10. Neil hasn’t invited me to the Broken Arrow ranch yet.
In the end, this comment from Karen sums up where many serious music lovers stand on the Bob vs. Neil debate:
“I love Neil Young. I am a fanatic. First and foremost, a Rustie (Neil Young fan). But I also love Bob Dylan.
“Neil has been very clear over the years on his own admiration and appreciation for Bob Dylan, he (Neil) has called Dylan the master on several occasions. Neil has said many times over that Dylan was an inspiration to him. One of the funniest, more recent comments was during a recent radio interview about Prairie Wind, Neil’s latest album, the interviewer had apparently heard that Neil does a great impression of Bob Dylan (presumably Dylan’s speaking voice, given the context of the interview.) Neil pauses, and as his manager literally breaks into the studio to make sure Neil is NOT going to impersonate Bob Dylan on air, Neil says, Impersonate Bob Dylan, huh? Hey, I’ve been doing that for forty years. Haven’t you been listening?”
Great comment. Makes it clear how Neil feels about Dylan. Neil Young is my Mecca, no one loves the man and his music more than I do, but we all should bow down to Mr. Bob Dylan. Noooo question. So. Whether you like Bob, Neil, both or neither, it’s all one song…”
“I’m listening to Neil Young, I gotta turn up the sound
Someone’s always yellin’, ‘Turn him down’.”
Bob Dylan’s Highlands (Copyright © 1997 by Special Rider Music)
You got too many secrets Bob Dylan said that Somethin’ like that”
Neil Young’s Bandit (Copyright © 2003 Silver Fiddle Music ASCAP)
 http://neilyoungnews.thrasherswheat.org/2010/08/vista-and-muse.html, The Vista and The Muse, Retrieved 11/25/2016