In an increasing number of cases it very much does matter which outbound se rver you use though for a particular domain given the restrictions imposed by the enforcement of some domain's SPF/DKIM configurations.
For example, earlier this year Yahoo changed their DMARC policy to p=reje ct thus instructing recipient MTAs to reject mail received from servers not covered by Yahoo's SPF/DKIM declarations. Hence, mail sent from a Yahoo do main from any server other than Yahoo's can end up being dropped. The fact that you might be able to successfully authenticate with your ISP's mail se rver etc matters little - you really do need to use Yahoo's servers if you want to send mail that appears to come from a Yahoo address (this is proble matic in the context of mailing lists but that's one for another discussion ).