Hi, Christine, and welcome.
I think your decision will come down to how near you want to get to the practical aspects of mechanical engineering, and also the size of organisation you see yourself working for. It also is affected by whether you want a full-time or part-time course, be employed or sponsored, or pay course fees.
Following a degree course will provide you with skills to go into design, then progression into customer facing or management roles.
If you take an apprenticeship, depending upon your prior qualifications, could lead you into technician level part time Certificate or Diploma level courses, which supplement what you would learn in your workplace. Diplomas may tend to be full time courses. There are two levels, (Ordinary) National Certificate or Diploma and Higher National Certificate or Diploma (ONC/D, HNC/D).
If you seek practical wokshop skills, you may follow the ONC route or take a National Vocational Qualification (NVQ) which assess what is learned in the workplace, where your competence is certified by internal and external assessors.
You can search on these abbreviations to find more info, but note that Scotland and Northern Irelands qualifications differ in their details from England, I'm not sure whether Wales offer their own.
If you can add more info, it's possible we could offer more focussed advice. This is without adding that mechanical engineering covers general engineering, aeronautical, motor vehicle and many other specialised fields, for which the units you would study may differ.
Good luck,
Bill