Excellent good.
So then:
X professes faith in Jesus Christ as his personal savior and does nothing going forward.
Y professes faith in Jesus Christ as his personal savior and does works.
They both die. All else equal, which one goes to Heaven?
re: “All else being equal, which one goes to heaven?”
Possibly both, possibly neither - it depends on what you mean by “professed faith” in Christ.
I’m not sure that you understand what professing faith, in the Biblical sense means.
It sounds to me that you believe “professing faith” is nothing more than an acknowledgement that something is true - i.e. that Jesus existed and that He is who He claimed to be - God’s Son, and that He died on the cross and rose from the dead.
You see, one may believe all those things to be true and yet, still not be a Christian. Believing a given set of facts are true does one no good unless one “acts” upon that belief.
For example, I may sit in a dark room and know intellectually that if I flip on the light switch, the lights will come on and I’ll be able to see. However, that knowledge does me no good until I physically go over and flip the light switch on.
So, you see, professing belief in Christ means much more than just believing some facts to be true. Recall how James pointed out that even the devil and demons “believe” and yet are not saved.
The reason demons aren’t saved is that even though they know and believe all the facts about Jesus to be true - they don’t profess/confess Him to be their Lord and Savior - they don’t allow Him Lordship, rulership, over their lives. It’s the same with people too.
See what Paul wrote in Romans 10:9-10 “that if you confess with your mouth, ‘Jesus is Lord’ and believe in your heart that God raised Him from the dead, you will be saved.”
The word “confess” means more than just an acknowledgement that something is true - it is an act of the will to not only admit that it is true, but to also place oneself under, to live by the truth you are confessing. To confess Jesus is Lord means to place oneself under His Lordship. He is to be Lord of your life - ones actions following that confession should give evidense as to whether you truely confesses Jesus as your Lord and Savior.