[Iarwain]

Well, let's look at this logically.

Eomer killed Ugluk in one on one combat, so we have:

Eomer>Ugluk

Eomer triumphed on the same battle field that Theoden was killed in, and Theoden was a fairly old man, so:

Eomer>Theoden & Ugluk

Sadly, that's as far as we can go by reason, because the others' skills were not tested against each other (especially Faramir), so within the bounds of reality, and without assuming, I would be able to confidently say that Eomer was better than Theoden and Ugluk, but Gimli and Faramir never fought on a scale that could be easily judged or compared.

If I could go outside the bounds of fact, and form a supposition, I might suppose that Eomer was also superiour to Gimli, because of his riding skills. Then, left with Faramir, I would say that Eomer was inferior as a captain, but superior as a fighter. So, in the end for fighting I would suppose that the ranks would be:

Eomer>Gimli>Faramir>Ugluk>Theoden

and for leadership skills I would rank them:

Theoden>Faramir>Eomer>Ugluk>Gimli

Iarwain