For tomorrow's City whizz-kids, the good news is that the investment banks and consultancies are hiring again. They may not be recruiting in the same numbers as before the recession but they are doing so more than last year.

As usual, post-MBA internships, often unpaid, are the key to getting a job. The top "bulge-bracket" investment banks tend to make their decisions in February, leaving the rest to the smaller boutique firms. Business school students compete ferociously for these placements.

In America, however, the tradition has been rather different. There, graduates are employed from university as analysts. They work hard at number-crunching for four or five years, leave to do a two-year MBA, and return as associates, the next rung up.

At least, that's how it used to be – but no more, according to a new book from Harvard Business School, Rethinking the MBA: Business Education at a Crossroads. These days, firms are training their own employees.

"Companies have increasingly been promoting from within. Many are actively discouraging their best young people from leaving lower-level positions for business school," say the authors, Srikant Datar, David Garvin and Patrick Cullen. At the same time, consultancies are taking non-MBAs at associate level from medical, law and other backgrounds. The non-MBA part of the mix is growing steadily. The authors say these changes were threatening the top US schools even before the recession.

In Europe, there is evidence banks are "growing their own" staff in some departments. The scale of the problem, however, appears to be smaller. "The Americans are used to the concept of people in investment banks leaving to do MBAs, whereas there isn't the same appetite for it here," says the head of recruiting at a London investment bank.

Derek Walker, head of careers at Saïd Business School, Oxford, agrees. In Europe, he says, the MBA is not seen as essential for banking in the way it has been in the US. "The MBAs that are hired here are those with transferable skills. Maybe they were working for a mining company, and after the MBA they go to a bank's mining team. In the consultancies, they are looking for quality of experience and critical thinking skills."

In financial services, he accepts the appetite for MBAs has been flat, but says that has opened the door to other organisations. "Good MBA students will always find themselves in demand," he says. "MBA programmes provide people with a tool kit and an aptitude and understanding of business."

At London Business School, which has the largest MBA class in Britain and is heavily geared towards financial services, careers director Lara Berkowitz accepts the trend. "Some banks have said they prefer to grow their own, particularly in sales and trading, or they're looking at highly quantitative people with PhDs," she says.

"While we see fewer banks with sales and trading associate level programmes in Europe, the banks have absolutely retained their MBA recruitment programmes for mergers and acquisitions and some also have asset management programmes. Banks are always going to want people who bring diversity and a fresh perspective to the City."

These trends highlight the dilemma of the MBA as a qualification: can an MBA course train an investment banker as efficiently as an industrial manager? Michael Luger, director of Manchester Business School, was recently in London where he and an alumni group saw the West End show Enron, about that company's rise and fall.

"It was brilliant," he says. "For me, it did raise questions about the ability to step back and think critically and broadly. And that's what the MBA should be doing. It's not a technical degree, it's about transforming you as a person and elevating you to the next level of management leadership."

The Judge Business School in Cambridge is bucking the trend. Karen Siegfried, MBA executive director, reports an increase in sponsored students from finance and consultancy firms. The explanation, she suggests, is that the 12-month Cambridge MBA provides a very different experience to that of the two-year US programme.

For a consultant who will need to manage clients, it appears to be accepted that a good business school with an international intake still provides the best training. But top-level banking is now so sophisticated that any MBA course would struggle to match the technical input of an in-house training scheme.

Does this matter? Huw Morris, chairman of the Association of Business Schools, says: "For the bulk of the MBA programmes as they're described in the guidelines issued by the accrediting bodies, the MBA is not a detailed qualification for work in high finance."

But he believes business schools have a useful role to play in educating the sales teams that boosted the growth of the financial sector after deregulation.

At Manchester Metropolitan University Business School, where Morris is dean, the finance Masters courses specialise in distribution and sales, and are "mapped" against the professional accounting and finance bodies.

At this level – professional qualifications – there are others who want to "grow their own" MBAs: law firms, for example. Amir Sharif, director of MBA programmes within Brunel Business School, points to Simmons & Simmons new "legal MBA" run by BPP College of Professional Studies. "It is entirely run as a commercial operation. They are just a training provider," he says.

How do the Harvard professors think business schools should respond to this? Employers, they say, want students with global perspective and leadership ability, good at integrating organisational realities and power politics. But they also want creative thinkers, good at oral and written communication. Since the crisis, they add, more lessons are needed on risk, regulation, restraint and the consequences of failure. And students need to be trained to question what they're taught.

Rethinking the MBA: Business Education at a Crossroads (Harvard Business Press) is published on 13 April