Haven't stayed in Kuwait. From reports above, both CY & JW are good choices.

Checking online, looks like the CY is only $20 cheaper than the JW. JW exec lounge is open longer than CY lounge (06:00-23:00). CY lounge is only open for a couple of hours in the evening. JW lounge says complimentary cocktails, but given Kuwait is a dry country think that just may be cut/paste from other lounge descriptions. You get points for incidental spend at JW & not at CY, so that may factor in if you think you might spend some $$ at the JW besides the room over the 6 weeks. Both properties websites are still showing free shuttle, although you might need to schedule them.

Putting aside the summer promo below, I'd probably opt for the JW because of lounge being open longer & incidental spend.

CY has a summer promo going; JW doesn't.

SUMMER OFFER - EXPLORE KUWAIT CITY WITH 3 FOR 2
Enjoy a free night when you stay 3 nights! Promotional rates are valid for bookings from May 15 – September 17, 2016, for stays from May 20 – September 10, 2016 at Courtyard Kuwait City Hotel.

Cheers.