I would say go for the Deloitte opportunity because it is an amazing opportunity, what sector within Deloitte by the way?
A lot of people who work for the big 4 normally do so for a few years and then go to industry, but the level work, the competition, the expectations of the big 4 are unlike pretty much all other firms which is why many many top jobs ask for big 4 credentials because it builds you up in that way. Just look at the careers of ex big 4 people and you will see what direction you can go towards.
So not sure what sector in Deloitte as you didn't say, but normally we value a degree with professional accounting qualifications (ACCA or ACA) more so than a degree and masters, as others have said, it is not going to boost your opportunities much. After you walk in to industry, degrees don't mean much, it is more of a entry requirement, after that what counts is your own professional development so it is probably correct in saying a masters isn't going give you much more.
Build yourself up, a years experience at Deloitte is like 2-3 years elsewhere. Build yourself up, look for invest opportunities, make some money, and opportunities to study will be available to you in the future, trust me. Universities aren't going anywhere, but opportunities like big 4 do not come by easily.
In a nutshell, the Deloitte opportunity far far outweighs the benefits (if any) of doing a masters now - but you can do it later so win win.