Gonna have a go at this...

Previously this product was offered by HLB but I think it has been discontinued, if I recalled correctly.

Base Lending Rate (BLR): 6.85%w.e.f. 16/07/2014
Base Rate (BR): 3.84% w.e.f 10/07/2015
Kuala Lumpur Interbank Offered Rates (KLIBOR): 3.73% (3-mnt KLIBOR based on previous business day.)

To your question:-
my Q is, how am I supposed to choose as each bank's Base Rate & the klibor rate ( I think it's called klibor rate [ BR + ** = rate % ] ) differ from each other... I mean, which should I look - the lower BR with higher klibor rate OR higher BR with lower klibor rate??

You don’t have to look at the KLIBOR rate because it will be the same across the board. Bank’s do not have “direct” control over the KLIBOR rate because it is a futures product traded via Bursa Malaysia Derivatives Berhad.

Focus on the spread the Banks are offering, the lower the interest rate will translate to lower interest payment for you. Nevertheless, look at the outcome.

Now to your last question:-
the rate ended with the same % though.... 

I think the outcome will generally be “more or less” be the same between BR and KLIBOR.

However, KLIBOR is a futures product so it might move “first” (either at a discount or premium) depending on circumstances (too many to describe). If at a discount, it will translate into savings and vice-versa.

Whereas, Base Rate is dependent on the OPR set by BNM. It’s more rigid and conservative as it is regulated by BNM.

That being said, though KLIBOR is exchange traded and OPR is regulated by BNM, KLIBOR is subordinate to OPR.

So why subscribe to KLIBOR loan? Due to market inefficiencies, it is possible that KLIBOR may be trader higher or lower. When such instances occur (especially when KLIBOR is traded lower), you will experience savings on the interest paid to the bank. However, over time the market will correct itself and the situation will become status quo again over time.