Granted, currently, too many Marriott members with lounge access and admittedly some are obnoxious. But we cannot fault the property for this and the situation will change with regards to the volume of elites in the next year.
The Banyan Tree was built in 1995 and last renovated in 2009, more than 10 years ago. The ICH Bangkok was built in 1998 and last renovated in 2009 also. While the MMQP was just recently renovated in 2017 upon its reflagging into the Marriott brand.
I have no experience at the Banyan Tree and thus I cannot comment on that property.
The basic rooms is much better at the InterContinental than the MMQP, even though in need of refresh. But I found the MMQP suites and their bathrooms to be bigger than the InterContinental.
Club access is guaranteed if you are a Marriott Platinum or higher at the MMQP while the IC Club is accessible only to Royal Ambassadors and people paid Club rates. IHG Platinums, Spires, and Ambassadors have to purchase access for $100++ per room per night. Food is better at M-Club but cocktails are superior at the IC Club.
Goji offers better breakfast experience and much better variety than Espresso.
Much larger and better pool at the MMQP even though the tiny rooftop pool (not infinity) at the InterContinental offers dramatic views of Bangkok.
Central location of the InterContinental makes it better situated.
Better redemption at the InterContinental especially if you do 4 for 3 and the 20% rebate (10% for having the CC and another 10% for being a paid Ambassador).
Both are great properties IMO but all depends on the nightly cash rates and your preferences.

Breakfast at Espresso

Breakfast at Goji