Scrapping air passenger duty (APD) in Wales could mean more than a million passengers a year would fly from Cardiff Airport rather than Bristol, the English airport has claimed.
Bristol Airport chief executive Dave Lees told MPs such a move would give Cardiff an unfair advantage.
He told the Welsh affairs committee said he wants a UK-wide APD reduction.
The committee is investigating whether APD should be devolved to Wales, allowing Welsh ministers to scrap it.
For years, the Welsh Government, which owns Cardiff Airport, has been asking for control of the tax, which has been devolved to Scotland and for long-haul flights from Northern Ireland.
But the UK Treasury has refused, insisting it would disadvantage airports in England.
In previous evidence to the committee, Exchequer Secretary to the Treasury Robert Jenrick said: "The [UK] government remains concerned about the impact of any devolution to Wales on English airports, particularly Bristol Airport which exists in a single aviation market with the largest commercial airport in Wales, Cardiff.
"The UK government must ensure that any decision does not disadvantage customers or businesses."
Mr Lees gave evidence to MPs in Cardiff on Thursday.
He said devolving APD to Wales, allowing Welsh ministers to scrap it, could mean that Bristol would lose more than a million passengers to Cardiff - he said that airlines would also move.
"I spoke to one of our key airlines yesterday and they said they would move capacity from Bristol to Cardiff very quickly, this isn't long-term, this is an immediate impact," he said.
Cardiff Airport chief executive Debra Barber said there were enough passengers to keep both airports busy but it would be positive for Cardiff.
"For us we think Cardiff would gain...initially between a hundred thousand to four hundred thousand [passengers] with a maximum of six hundred thousand by 2025," she said.
"There would be a material economic benefit for south Wales," she added.
Welsh Government finance minister Rebecca Evans told MPs: "We've been calling on the UK government for some time to devolve air passenger duty to Wales."
She added: "There was unprecedented, I think, support and single-ness of mind on this issue across Welsh Government and across Wales much more widely."
Committee chair, Conservative Monmouth MP David Davies, asked the minister whether there were any calls in Wales for APD to be increased.
"None that I've heard," the minister replied.
Air passenger duty - a brief history
Travel expert Simon Calder told BBC Radio Wales' Good Morning Wales programme air passenger duty was introduced in 1995 by the then Tory chancellor Ken Clarke, "who told me later he that he just thought that people who fly on planes should probably pay a bit of tax".
"If you were flying, say, from Cardiff to Tenerife or Edinburgh you'd pay £5, £10 for long haul.
"The tax has proved incredibly popular with a succession of chancellors because it's really easy to collect because the airlines do all the work, it's almost impossible to avoid and half the people who pay it don't vote in Britain because, of course, they're foreign visitors.
"So it's increased relentlessly, that Cardiff to Edinburgh return is now £26 and going long haul, for instance Cardiff to Doha, is £78 in economy from 1 April, in business class it will go up to £172 so quite a tax.
"The thinking is that if Wales were able to take control of Air Passenger Duty it could set the amount at a level which would actually encourage aviation within Wales.
"They're talking about a range of Welsh airports but I think we really mean Cardiff."