Which rank is senior in the Army, Master Sergeant or First Sergeant?

I'm sort of confused by your questions but I think what you're asking is which rank is higher than the other. So both Master Sergeant and First Sergeant are the same pay grade which is E8, however First Sergeant is senior to and outranks Master Sergeant. You can tell the difference between the two being that a Master Sergeants rank has 3 Chevrons and 3 Rockers, the First Sergeants is the same but with a Diamond in the center. The First Sergeant is the Senior Non-Commissioned Officer of a Company and assists the Company Commander which is usually a Captain.

A Master Sergeant usually assists or is in charge of an office at the Battalion or Brigade level, sometimes a Master Sergeant will be in charge of a Detachment or a School. A Detachment is smaller than a Company. A School is literally that, a place designated where Soldiers conduct designated training.

EDIT

Didn't see that SGM Dawson beat me to the punch, his explanation is good follow that.

Both are an E8 pay grade. First Sergeant is a "Command" position, working for a Company commander. There is normally 4 platoons in a Company plus a Headquarters section. The 1SG is the Senior NCO of the Company, the CDR's right hand in keeping him in touch with the enlisted/NCOs of the company.
A Master Sergeant is in a position of authority, usually a section leader, shift leader in a Headquarters or similar type of unit, usually a Non Commissioned Officer in Charge(NCOIC) of a section. The MSG position is usually found in Battalion or Brigade level staffs, or sometime there are units which are not big enough to be a company, they are called detachments. Detachments are not usually rated to have a First Sergeant but a Master Sergeant. When in this position, the MSG is usually sent to 1SG school as the MSG in addition to his unit duties will perform the 1SG duties as well.

Neither they are the same. One may have a position over the other but it can go either way.

Confus-tion. MSG is E-8. 1Sgt CAN be SFC, E-7, or 1Sgt, E-8. Of course an E-8 "outranks" an E-7, but, and here is the rub, if the E-7 is in a 1Sgt slot, then by tradition, he "outranks" a Master Sergeant only in the performance of his duties at Company level. He is the "Daddy" of the company. The MSG could be Battalion Ops, or Brigade or even Divisional, but at the Company level, the 1Sgt is ranking in his position. If they are both E-8's, then the one with the earliest promotion date is Senior. And most Senior NCO's are adept at accepting "who's in charge" where and when. You don't reach those ranks alienating your peers. Either way, to reach that Senior NCO rank demands respect.

This is similar to a CSM and the S-3 SGM - both are Sergeant Majors, Both are E-9's just the duties and responsibilities are very different. Technically the CSM is senior to the Ops SGM, but their ARE situations where the OPS SGM has more authority then the CSM. Same with 1SG and MSG. The few times you may see both a 1SG and a MSG in the same company is when you are dealing with a HHC company. You may have a MSG in charge of the S-3 daily operations, or Motor Pool. It is extremely rare to have 2 E-8's in a line company.

First Sergeant, by billet, is senior.

Congress has spoken on this, First Sergeant! A Master Sergeant is referred under UCMJ as a Sergeant... only First Sergeants and SGM
Are referred to as First Sergeant or Sergeant Major. Why? First Sergeants only real focus is taking care of the troops and families. There is no greater challenge nor greater award them being a First Sergeants. Master Sergeants quite frankly piss me off. It’s all about them, their narrow professional interest. There is no greater role than that of a committed First Sergeant 100% committed to taking care of soldiers and families. Airborne