Firstly welcome to the world of SEO, but the answer is pretty simple and I don't know why anyone who knows SEO would tell you any different.
If your site / CMS allow is, have them all on your site otherwise you are creating more work for yourself.
If the articles are on your site, the DA will pass down to the article pages. Google ranks pages based on your customer experiences, so if they have visited a blog article on your site through a long tail keyword and then want to actually purchase your services. If they type in 'x', Google will remember they have been to your site and interacted (so long as it looked like they had a good experience) Google will rank your other pages higher, potentially leading to more conversions and traffic.
Also you only have one brand to manage and not two, if someone wants to link to one of your detailed and informative blog articles then this link also passes weight back to your home page.
I would always say where possible have the blog on your main site, the only time I would suggest not to is if your current site can't support it.
Hope this is useful, I have only given the key reasons why you should put it on /blog (and it doesn't have to be called blog, you can name it anything you like, articles etc). But there are far more reasons for keeping it all on one domain.
Without knowing the company that recommend putting it on a new site I feel unfair commenting about them, but maybe they was thinking they could get you to pay for a brand new additional site and get some extra revenue for themselves - like I said I don't know them so don't like commenting about other peoples businesses if I don't know them - but that would be my only logical thinking of why they would want you to have a second site.
Thanks
Andy