I'm a bit biased since i'm the cofounder of such an e-mail service (called ubivox). However I shall try to be as objective as possible.
Depending on the mail server your magento system is relaying it's e-mail through the answer is both yes and no.
If you're not sharing your outgoing e-mail server (SMTP) with anybody else and you do general maintenance on it to keep it off black lists etc, you might save some money by using magento.
If words likes feedback loops, Black lists, SPF, Domain keys, bounces etc are latin/greek in your ears, then please use a professional e-mail list sender if your bulk e-mailing is important for your business.
Most bulk mail companies spend a lot of time ensuring the reputation of their sending email servers, keeping them out of black lists etc. This work is extremely time consuming if you have to do it on a one person basis, and almost impossible if you are hosted on a standard web hotel platform with a shared SMTP mail server, used by thousands of other people.
Furthermore an bulk email service is specialised in tracking opens, clicks, devices etc, often giving you a much better statistical material to evaluate your success.
Sending out thousands of emails with images requires that your image hosting server is capable of handling the amount of request that might come seconds after the mails has been delivered. (most bulk providers host your images on specialized servers for that reason).
Sending bulk e-mail, or doing email marketing in general is so much more than just blasting a lot of emails into peoples inboxes. Having a complete and reliable turn key system for handling those process (collecting, sending, designing, measuring, handling unsubscriptions etc), with a support department which can help you with questions is in most cases a really good business choice, since you can let your email service provider be experts in that field and you can concentrate on writing good e-mails and keeping in touch with your loyal customers.
Often the money saved by "doing it yourself" is peanuts compared to the time wasted by trying to replicate the systems you get by using a professional bulk email sender.
Mostly because keeping up a good sending reputation takes a high volume of emails sent each month and a lot of man hours to tweak the sending servers for each email hosts special rules and needs. Using an email service splits this cost amongst a lot of customers, and the basic monthly work is almost the same whether you are one sender or thousands.