It depends on your business. Is your potential audience even on Twitter? Do they take kindly to cold emails? Are you just looking for 5 huge, $10k a month clients? So, it all depends on that.

For the sake of argument, I'm going to assume you're offering something for around $50 that over 10k people can and should use … they just don't know it exists yet.

Now, to answer your question – normally, from a sales conversion standpoint, email tends to outperform most other online mediums like Twitter.

However, you throw in a key phrase, “potential users.”

So, it sounds like you're still in the “outreach” phase and here's what I would do …

I would use both.

LAME! I know, but hear me out.

Using email for outreach can be good in some scenarios like trying to get reach hot prospects, but it does not scale well. You're not going to be able to email 10k people … ever. Well maybe within about 3 years you could … but that would really suck.

So, I would only use email for outreach in an attempt to land influencers. You know, the big guys and gals with the big audiences … where if they like your product/service … they'll recommend it to their audience. And, more than likely, you'll want to give your product/service to them for free.

Otherwise, I recommend setting up a landing page with an opt-in form, lead magnet, the whole shebang … with a follow up email series that sells your product/service.

I would then use Twitter … because, Twitter is powerful and allows you to communicate with people, participate in conversations, etc and can get you in front of a lot of people.

Anyway, I'd use Twitter to send people to that landing page where you would collect their email address.

To summarize. Use email outreach to land influencers. Create an email follow up series to convert leads into customers. Get leads from being hyperactive on Twitter.