Yes, you will lose resolution. The only way you won't, is to export something using the exact same settings as the original material. And that won't work on the web.
H.264 does a good job but, like all things involving compression, is a bit of a dark art. If the material is headed to the web, you are dealing with three things - image size, data rate and image quality - with data rate the most restrictive. Only you can find the balance between the three that works for your clients.
x