There is a bit to consider. Do you want to target keywords which will also help with seo with an exact site description in the name? Do you want a brand? Is the brand available in both dot com and .eu? Are the most generic names taken? Can you get something short an abbreviation? LLL.eu. What is the industry your targeting?
.eu domain is great if your market audience is strictly Europe or you have a business that has anything to do with European institutions/projects. If your service is not location restricted, then .com is always better to remember.
I don't really know what the market is like in the EU. Are they more educated to remember .eu or are they more familiar with .com. I live in Australia where the domain is .com.au however I've always opted in for .com because it is easier for people to remember. I would say choose whatever people will remember easier. And off course if you ever think you might go global then definitely choose the .com
Yes it is good if your target audience if only EU area, but if you target audience is global and for some services/product you wanted to target EU, then go with Multilingual sites, make your main domain .com and the can target a number of Areas with other domain extension or Can create a directory for such audiences.