will Bitcoin still have value if banks adopt the underlying technology?

[Dabs]

Think of the bank's own coin as a side-chain. You'll eventually have exchanges trading bitcoin for bankcoin.

[franky1]

do bank customers care if their funds are saved on a mySql database, a MSaccess database, or a blockchain.. no..

bank customers dont care about the technology behind banks.
fiat will always be fiat no matter how its stored

only a few smart people will be interested in the lack of security, lack of assurance and lack of openness.. and those people would usally move their funds away from fiat, not matter how the fiat was stored

[Kakmakr]

There are a big difference between a Public Blockchain <Bitcoin> and a Private Blockchain <Banks> In a public Blockchain everything is transparent and open to the public and it's development is not in control of a single entity. In a private Blockchain, their is NO transparency and the banks control the parameters of the development and the changes to the code.

So who would you trust between these two technologies? 

[zimmah]

with increasing number of financial institutions showing an interest in the underlying technology of Bitcoin rather than the coin itself, could it be possible Bitcoin becomes irrelevant in the future, most people are confident dealings with banks and if they offer similar technology why the need of Bitcoin.

The technology is only part of what nake Bitcoin good

The important part of what makes Bitcoin good is that it is decentralized,

If banks use the technology, they're still centralized, it will improve banks, but it will still be worse than Bitcoin.

[Indrawan77]

Both of them is important, but they dont related, the function of bitcoin is to store fiat while bitcoin is digital money
Bitcoin has its own advantage so no need to be afraid that bank is going to replace bitcoin