"I'll miss the quirky, intelligent humour he brought to the table. He was top shelf as far as cricket is concerned, as good as I've seen," Border said.
"Technically, he was absolutely fantastic. He had a presence at the crease and if you combine that with the cricket smarts he possessed you're going to have a pretty good package.
"It's a pretty simple formula, and he had it in spades."
Among Crowe's most memorable innings was his century against Border and Australia in the opening game of the 1992 World Cup at Eden Park.
New Zealand went on to win the match by 37 runs.
He rated Crowe's captaincy highly and maintained if Crowe had been fit during the World Cup semifinal against Pakistan at Eden Park in 1992 New Zealand would have won that match.
A hamstring injury meant he was unable to take the field for the second half of the match, which Pakistan won with a late flurry of runs from Inzamam-ul-Haq.
Border puts Crowe in the same bracket as the man widely regarded as Sir Richard Hadlee.
"It's one thing to take the wickets but someone's got to score the runs as well. Those two, when they were playing in the same team, New Zealand were a very very competitive team."
And Border also had a soft spot for the off-field Crowe, with whom he shared conversation, and the odd beer.
"He was just a tremendous bloke, really good company. I enjoyed many chats over a beer whether it be after cricket matches or at the golf course or socially generally. It's a very sad day."
Earlier, Prime Minister John Key paid tribute to Crowe.
"Today is a very sad and tragic day, not only for Martin Crowe's family but for New Zealand and indeed for the sport of cricket.
"He is a New Zealander who had a fan base not only right across the country but in fact right across the world.
"I think he'll be remembered for his remarkable talent, for the incredible 299 he scored against Sri Lanka, and for having the most number of centuries that a New Zealand batsman has scored.
"But most of all, people's hearts were touched by the battle that Martin Crowe had with leukaemia [and] his burning side desire to be there for the first game of the Cricket World Cup ... In New Zealand.
"Our great sympathies go to Lorraine and his children."
1968 - joined Cornwall Cricket Club, establishing a lifelong link.
1976-1980 - attended Auckland Grammar, becoming deputy head boy in his final year and, in addition to cricket commitments, a wing in the first XV.
January 19, 1980 - made his first-class debut for Auckland v Canterbury at Eden Park, aged 17 years and 119 days, scored 51 in maiden innings.
June 12, 1981 - first appears in the New Zealand Herald, relating to his century for the MCC Young Cricketers in a one-day match against an MCC XI which included former England captain Colin Cowdrey. Crowe was on a six-month scholarship with the Lord's ground staff.
February 13, 1982 - made one-day international debut v Australia at Auckland, did not bat.
February 26, 1982 - made test debut v Australia at Wellington, run out for nine.
February 4, 1991 - completed New Zealand's highest test score of 299, a feat that lasted 23 years. In doing so, participated in a world record partnership of 467 with Andrew Jones for the third wicket. Named sportsman of the year in relation to the feat.
February-March 1992 - captained New Zealand to the semi-finals of the 1992 World Cup at home, wins player of the tournament for his inspirational batting and innovative captaincy.
June 16, 1994 - made his second test century at Lord's; remains the only New Zealander to score more than one in 84 years and 17 visits.
July 5, 1994 - made his 17th and final test century v England at Manchester, still a national record.
July 1995 - published first autobiography Out On A Limb.
November 12, 1995 - completed his 77th and final test v India at Cuttack, caught for 15.
November 26, 1995 - completed his 143rd and final ODI v India at Nagpur, stumped for 63.
1995-2002 - invented, developed, marketed and broadcast Cricket Max, the pre-cursor to Twenty20.
1997 - joined Sky Television and worked as a cricket commentator, eventually rising to executive producer by his 2012 exit. Brought regular weekly broadcasts of First XV rugby to screens for the first time, along with other notable documentary series such as The Chosen Ones and The Mantis And The Cricket.
2001 - inducted into the New Zealand sports hall of fame and awarded an MBE for services to cricket.
April, 2003 - daughter Emma is born.
2006 - became the first New Zealander invited to deliver the annual 'Cowdrey Lecture' at Lords, on 'the spirit of cricket'.
November 5, 2011 - returned to club cricket for Cornwall reserves with the aim of being selected for Auckland and hauling in the 392 runs required to take him to 20,000 at first-class level. Fifteen days later the bid was over as he iced a left thigh muscle at 4am on the Sunday morning.
October 2012 - diagnosed with follicular lymphoma.
December 7, 2012 - tweeted he had burnt his New Zealand blazer after the treatment of Ross Taylor after his demotion as national captain, an action he later said was metaphorical.
June 2013 - announced chemotherapy treatment had restored him to normal health.