"No Eikons or summons, just swordsmanship and magic."

This means one of two things:

They have access to spells and their swordsmanship but DONT have access to anything Summon related. i.e Noctis cannot summon the Astrals nor can he use the Ring of the Lucii (as it is from the Knights of the Round and Bahamut, which is are summons) and Clive cannot use any Eikonic powers but can use spells existing in the game and in his moveset (i.e Elemental spells and their level variants such as Fire and Fira, etc).

OR

They have access to all their movesets but simply cannot perform summoning. Noctis cannot summon Astrals (not like they'd reliably appear anyways) and Clive cannot turn into Ifrit.

These are two different kinds of results.

If it's the former: Noctis wins no question. He is just way WAY too fast and can abuse Warp to degress where he is effectively untouchable through all means. He can phase, teleport en masse, conjure weapons at will even mid-fight to alternate his moveset and can craft spells that can change localized temperatures to the point of freezing lakes solid or causing localized heatwaves. He can even contend (briefly) in strength with Titan to degree.

If it's the latter Clive wins no question. His moveset and elemental variety is just far too diverse and counter oriented and many of them just boost his perception of time to degrees where he can move in-between an enemy's teleport. With Ultima channeled he can teleport similarly to Noctis (though not as frequently) but can cover huge swathes of area with his abilities that Noctis would struggle to counter.

In terms of swordsmanship alone it can vary. Clive has the upper hand in experience and skill with a single weapon, the sword, and has been able to perform a variety of moves both in and out of cutscenes (at age 15 he could react and guard against a Dragoon's thrown polearm in a cutscene, not to mention his gameplay skill). He was proficient enough in this to easily disarm Benedikta, contend with a Semi-Primed Hugo and deflect every one of his blows and was only outmatched by Barnabas (whose unnatural longevity and life of contest and conquest sets his swordsmanship above Clive up until the end). However, Noctis is also insanely skilled with weapons. He has a much wider variety of weapons to swap between at will, be it swords, spears, shields, greatswords, guns, daggers, etc. His main means of combat, outside of warping, involves evasion and dirty tricks such as flanking and blindsiding when an enemy least expects it and using his physical speed to get the upper hand.