Firstly, congratulations to your DS on securing two attractive offers. Contrary to popular opinion, apprenticeships (at L4 as well as L5-7) are limited and keenly contested by applicants.
I think a first port of call is for your DS to contact Deloitte and, in parallel, the other employer and clarify a couple of key points - or glean them from any offer paperwork/other info that has already come through.
Will his employment contract be 'permanent' (ie he rolls into a post-qualification role so long as he passes the course elements) or does the contract only guarantee employment for the duration of the training?
What is the specific course he will enrol on, alongside his 'day job'; who is the course provider; what content is covered and how is the teaching delivered (weekly/block; f2f/online)?
In the case of Deloitte, what realistic prospects does he have to undertake further study at L5-6 (ie degree or degree equivalent). Deloittes may say that excellent progression will not be inhibited by lack of L5-6 but then he should, perhaps, ask for concrete examples of this having been the case in the team/functional area he will be joining.
Has he already got a feel for the culture of each employer and the types of clients and projects handled? Setting organisation 'name' to one side for the moment, which role potentially excites him the most?
Finally, are both roles in the same specialist area or is the degree apprenticeship broader and more generalist (at least initially) in scope? Does that matter to your DS now or potentially in the future?
I have a DC undertaking a degree-level apprenticeship (different sector) and they drilled down into the issues I have identified above. Prospective employers don't mind being asked these questions (as often these details only emerge at the offer stage) as they'd much prefer to take on someone who has properly considered the role - which typically require a lots of maturity, resilience and professionalism from the very first day.
Only your DS can decide but perhaps clarification of some of the issues identified above might help determine the tricky trade-off between L4 with 'name' and L5-6 with 'lesser name'. I hope that helps.